17.3 CHAPTER 17. TRIGONOMETRY
SOLUTIONLHS =
1 − sin x
cos x
=1 − sin x
cos x×
1 + sin x
1 + sin x=
1 − sin^2 x
cos x(1 + sin x)=cos^2 x
cos x(1 + sin x)
=cos x
1 + sin x= RHS
Exercise 17 - 8
- Simplify the following using the fundamentaltrigonometric identities:
(a) tancos θ θ
(b) cos^2 θ.tan^2 θ + tan^2 θ.sin^2 θ(c) 1 − tan^2 θ.sin^2 θ(d) 1 − sin θ.cos θ.tan θ(e) 1 − sin^2 θ(f)�
1 −cos^2 θ
cos^2 θ�
− cos^2 θ- Prove the following:
(a) 1+sincos θ θ= 1 −cossin θ θ(b) sin^2 θ + (cos θ− tan θ)(cos θ + tan θ) = 1− tan^2 θ(c) (2cos(^2) θ−1)
1 +
1
(1+tan^2 θ)=
2 −tan^2 θ
1+tan^2 θ
(d)cos^1 θ−cos θtan
(^2) θ
1 = cos θ
(e)2sinsin θ θ+coscos θ θ= sin θ + cos θ−sin θ+cos^1 θ
(f)
�cos θ
sin θ+ tan θ
�
. cos θ =sin^1 θ
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