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430
@surajpandey said:
hi puys back with some more trigo,...
hope that will be concept maker for you.
i m trying to put variety of questions on trigo. that can help you out in all the manner.
1.),
sinx=21/29, find the value of secx +tanx
if x lies b/w 0 and 90.
a 1
b pie/1
c 5/2
d none of these.
2.)
if A is in the fourth quadrant and cosA = 5/13, find the value of (13sinA +5secA)/(5tanA +6cosecA)ďťż
a -2/37
b -3/27
c 2/37
d cant be determined
3.)
5 sin^2x +3cos^2x=4, find the value of sinx and cosx
a +/- 1/rt2 and +/-1/rt2
b +/-rt3/2, +/- rt2
c rt3/2, 1/rt2
d none of these
4.)
calculate x, when x is 0
2 sin^2x + 4cos^2x=3
a 30
b 60
c 45
d none of these
5.)
find the value of tan75
well i will not give options in this one..
please put your answers.
well guys there could be thousand ways but will separately post the best answers and will share at this group or at fb.


giving my thought process here..

1) sin x = 21/29= Perpendicular / Hypotenuse. So definitely other side will be shorter and its value will be 20, as it is a set of Pythagoras Theorem values, 20, 21 & 29

So now we have right angled triangle, values of sec x = 29/20 and tan x= 21/20

Putting in equation:- sec x + tan x = 5/2




2) First while solving in "Tashaan", i had not looked '4th' Quadrant is given, obviously answer did not match, so looked over again and felt like wasted 2 mins.

Quadrant Concept:-
1st Quadrant= All values are Positive
2nd Quadrant= Sin and cosec values are positive, and others are negative.
3rd Quadrant= Tan and Cot values are positive, and others are negative.
4th Quadrant= Cos and Sec values are positive, and others are negative.

Applying the same, Cos A= 5/13, again apply Pythagoras in Rt. angle triangle, gives set of 5, 12 and 13.

Sec A= 13/5, Sin A= - (12/13) , cosec A= - (13/12), Tan A= - (12/5)

Putting values in equation
(13sinA +5secA)/(5tanA +6cosecA)ďťż = - (2/37)

431
@anticipator.lad said:
giving my thought process here..
1) sin x = 21/29= Perpendicular / Hypotenuse. So definitely other side will be shorter and its value will be 20, as it is a set of Pythagoras Theorem values, 20, 21 & 29
So now we have right angled triangle, values of sec x = 29/20 and tan x= 21/20
Putting in equation:- sec x + tan x = 5/2
2) First while solving in "Tashaan", i had not looked '4th' Quadrant is given, obviously answer did not match, so looked over again and felt like wasted 2 mins.
Quadrant Concept:-
1st Quadrant= All values are Positive
2nd Quadrant= Sin and cosec values are positive, and others are negative.
3rd Quadrant= Tan and Cot values are positive, and others are negative.
4th Quadrant= Cos and Sec values are positive, and others are negative.
Applying the same, Cos A= 5/13, again apply Pythagoras in Rt. angle triangle, gives set of 5, 12 and 13.
Sec A= 13/5, Sin A= - (12/13) , cosec A= - (13/12), Tan A= - (12/5)
Putting values in equation
(13sinA +5secA)/(5tanA +6cosecA)ďťż = - (2/37)
nice bro!! cheers
1st one is nice.
well want to know one thing.
will base always be the shorter one? i mean can perpendicular be less than base like you mentioned in the statenment that "other side will be shorter".

2nd one
yes that happens most of the time with us.
so its necessary for us to remember all the formula from trigo thoroughly.

rest we all know.
IF i say about the shortest one then more or less you can solve it within 1 minutes.

try next 3.
432
@surajpandey said:
hi puys back with some more trigo,...
hope that will be concept maker for you.
i m trying to put variety of questions on trigo. that can help you out in all the manner.
1.),
sinx=21/29, find the value of secx +tanx
if x lies b/w 0 and 90.
a 1
b pie/1
c 5/2
d none of these.
2.)
if A is in the fourth quadrant and cosA = 5/13, find the value of (13sinA +5secA)/(5tanA +6cosecA)ďťż
a -2/37
b -3/27
c 2/37
d cant be determined
3.)
5 sin^2x +3cos^2x=4, find the value of sinx and cosx
a +/- 1/rt2 and +/-1/rt2
b +/-rt3/2, +/- rt2
c rt3/2, 1/rt2
d none of these
4.)
calculate x, when x is 0
2 sin^2x + 4cos^2x=3
a 30
b 60
c 45
d none of these
5.)
find the value of tan75
well i will not give options in this one..
please put your answers.
well guys there could be thousand ways but will separately post the best answers and will share at this group or at fb.
3)
Its an option play. Answer is A

If someone still need it solution by old method then,
5 sin^2x +3cos^2x=4
=> 3(sin^2x + cos^2x) + 2sin^2x= 4
=>2 sin^2x =1
+> Snx = +/- 1/ rt2 same for cosx...so option goes A.

4) same concept
2(sin^2x+cos^2x)+ 2 cos^2x = 3
=> cos x = 1/ rt2; x=45

5) tan (45 + 30)= (tan 45 + tan30) / (1- tan 45 tan30) = 2+ rt3




433
@anticipator.lad said:
3)
Its an option play. Answer is A
If someone still need it solution by old method then,
5 sin^2x +3cos^2x=4
=> 3(sin^2x + cos^2x) + 2sin^2x= 4
=>2 sin^2x =1
+> Snx = +/- 1/ rt2 same for cosx...so option goes A.
4) same concept
2(sin^2x+cos^2x)+ 2 cos^2x = 3
=> cos x = 1/ rt2; x=45
5) tan (45 + 30)= (tan 45 + tan30) / (1- tan 45 tan30) = 2+ rt3
you got all questions rght.


now answer my query in last post.

if anyone else has got any problem..please ask me or anticipator bhai.

434
@surajpandey said:
nice bro!! cheers 1st one is nice. well want to know one thing. will base always be the shorter one? i mean can perpendicular be less than base like you mentioned in the statenment that "other side will be shorter".2nd one yes that happens most of the time with us. so its necessary for us to remember all the formula from trigo thoroughly.rest we all know. IF i say about the shortest one then more or less you can solve it within 1 minutes.try next 3.
Sorry, i wanted to say

So definitely other side will be shorter * than 29 (hypoteneus) *

No its not necessary that base will be shorter...its my mistake... Sorry again.
435
As value of Tan lies in between ( minus infinity to infinity ), it can be greater or lesser value at base...

@surajpandey
436
@anticipator.lad said:
As value of Tan lies in between ( minus infinity to infinity ), it can be greater or lesser value at base...
@surajpandey
OK bro... ab agar aapke pass aur trigo ke ache question hai toh share karo..
milke karte hai..nahi toh aaj raat mein mein aur karunga...

jab tak poora khatam nahi karunga quantum cat ke question tab tak aage nahi badhte .. ok?
437

Number of Integral Values of x for which sin A = (4x - 3) / 9 ,


where A lies in between 0 and 90, both 0 and 90 are inclusive.

Options:-

A) 5
B) 4
C) 3
D) 2

CGL- TIER 2- 2012 QUESTION.

Please explain me as I am confused and getting two answers, which can't be possible.
438
@anticipator.lad said:
Number of Integral Values of x for which sin A = (4x - 3) / 9 ,
where A lies in between 0 and 90, both 0 and 90 are inclusive.
Options:-
A) 5
B) 4
C) 3
D) 2
CGL- TIER 2- 2012 QUESTION.
Please explain me as I am confused and getting two answers, which can't be possible.
bhai answer 3 aa raha hai?
439
@anticipator.lad said:
Number of Integral Values of x for which sin A = (4x - 3) / 9 ,
where A lies in between 0 and 90, both 0 and 90 are inclusive.
Options:-
A) 5
B) 4
C) 3
D) 2
CGL- TIER 2- 2012 QUESTION.
Please explain me as I am confused and getting two answers, which can't be possible.
bhai ans should be 3 ... as ....0

solve and we get 3/4
440

@sampras said:
bhai ans should be 3 ... as ....0
solve and we get 3/4
finally got it...
441

good Job @surajpandey , @anticipator.lad and @coolparul007 .... All the Best ... may you put up your Best... and achieve SUCCESS

442
@sampras We have learned from the Best bhai... 😃 and the best is you!
443

kyunki yaha pe maine x=0 rakha toh equation ki value -1/3 not possible.


x=1 equation= 1/9 could be possible as value of x lie between 0-1)

x=2 equation = 5/9 again b/w 0-1

x=3 equation ki value 1 as you said 1 is inclusive

x=4 value will be greater than 1.

so only x=1,2 and 3 is possible.,

444
@anticipator.lad said:
@sampras We have learned from the Best bhai... and the best is you!
together we are Best dear...
445
@sampras said:
good Job
@surajpandey , @anticipator.lad and @coolparul007 .... All the Best ... may you put up your Best... and achieve SUCCESS
thanks bhaiya..we willl try our best to get whats the best.
446

hi guys some awesome trignometry question incase you have brush ups your basics.


click this link



447
@surajpandey said:
hi guys some awesome trignometry question incase you have brush ups your basics.click this link
ban gaye saare?
448

sin^2x +cos^2x +sec^2x +cosec^2 + tan^2 +cot^2
iski minimum value?
a 5
b 1
c 7
d 3

449
@surajpandey said:
sin^2x +cos^2x +sec^2x +cosec^2 + tan^2 +cot^2
iski minimum value?
a 5
b 1
c 7
d 3
(sin^2x +cos^2x) +sec^2x +cosec^2x + (tan^2x +cot^2x)
= 1 + sec^2x +cosec^2x+ (sec^2x -1+cosec^2x - 1)
=2(sec^2x +cosec^2x) - 1
= 2(1/cos^2x + 1/sin^2x) - 1
= 2{1/(sin^2x cos^2x)} - 1

To get Minimum value ; as denominator (sin^2x cos^2x) should be maximum; which is possible at 45 degree. Because for 0 and 90, the denominator gets 0 and value will goes to infinity. So putting x=45 degree

(sin^2x cos^2x= 1/4; maximum value

Minimum value of
= 2{1/(sin^2x cos^2x)} - 1
= 2(4)- 1 = 7