Inverse Trigonometry QA 5
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This document contains two problems from inverse trigonometry. The first problem involves finding the values of x and y given trigonometric expressions involving tan(x) and tan(y). The second problem proves the identity x = -x + pi for x in the range (-pi, pi). Both problems are solved step-by-step using trigonometric identities and properties. The document also provides contact information for the physics help website.
![Inverse Trigonometry 5
Physics Helpline
L K Satapathy
Question :
Answer
2
1 1
2 2
11 2tan sin cos , 1, 0, 1
2 1 1
yxFind the value of x y xy
x y
2
1 1
2 2
11 2tan sin cos
2 1 1
yx
x y
1 11tan [sin (sin 2 ) cos (cos2 )]
2
tan tan1tan (2 2 ) tan( )
2 1 tan .tan 1
[ ]
x y
xy
Ans
2
1 1
2 2
1 tan1 2tantan sin cos
2 1 tan 1 tan
Putting x = tan and y = tan](https://image.slidesharecdn.com/invtrig-161024154706/85/Inverse-Trigonometry-QA-5-2-320.jpg)
![Inverse Trigonometry 5
Physics Helpline
L K Satapathy
Question :
Answer
1 cos, tan , ,
1 sin 4 2 2 2
x xProve that x
x
2 2
1 1
2 2
cos sin
cos 2 2tan tan
1 sin cos sin 2sin cos
2 2 2 2
x x
xLHS
x x x x x
2 2
1 1
2
cos sin cos sin
2 2 2 2tan tan
cos sincos sin 2 22 2
x x x x
x xx x
1 1
tan tan
4 2tan tan tan
4 2 4 21 tan tan
[ ]
4 2
x
x RHx S
x
](https://image.slidesharecdn.com/invtrig-161024154706/85/Inverse-Trigonometry-QA-5-3-320.jpg)
Inverse Trigonometry QA 5
- 1. Physics Helpline L K Satapathy Inverse Trigonometry 5
- 2. Inverse Trigonometry 5 Physics Helpline L K Satapathy Question : Answer 2 1 1 2 2 11 2tan sin cos , 1, 0, 1 2 1 1 yxFind the value of x y xy x y 2 1 1 2 2 11 2tan sin cos 2 1 1 yx x y 1 11tan [sin (sin 2 ) cos (cos2 )] 2 tan tan1tan (2 2 ) tan( ) 2 1 tan .tan 1 [ ] x y xy Ans 2 1 1 2 2 1 tan1 2tantan sin cos 2 1 tan 1 tan Putting x = tan and y = tan
- 3. Inverse Trigonometry 5 Physics Helpline L K Satapathy Question : Answer 1 cos, tan , , 1 sin 4 2 2 2 x xProve that x x 2 2 1 1 2 2 cos sin cos 2 2tan tan 1 sin cos sin 2sin cos 2 2 2 2 x x xLHS x x x x x 2 2 1 1 2 cos sin cos sin 2 2 2 2tan tan cos sincos sin 2 22 2 x x x x x xx x 1 1 tan tan 4 2tan tan tan 4 2 4 21 tan tan [ ] 4 2 x x RHx S x
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