Given:
tanθ = 7/8
⇒ Assume in a right triangle:
height = 7, base = 8, hypotenuse = √113
sinθ = 7/√113, cosθ = 8/√113, cotθ = 8/7
Now the expression:
[(1 + sinθ)(1 − sinθ)] / [(1 + cosθ)(1 − cosθ)(cotθ)]
= (1 − sin²θ) / [(1 − cos²θ)(cotθ)]
= cos²θ / [sin²θ · cotθ]
= cos²θ / [sin²θ · (cosθ/sinθ)]
= cos²θ / (sinθ cosθ)
= cosθ / sinθ
= cotθ
= 8/7
Thus the answer = 8/7
Important Questions from Trigonometric Identities
What is cos 2β equal to ?
What is the value of sec2γ?
On simplifying \(\frac{{{{\sin }^3}{\rm{A}} + \sin 3{\rm{\;A}}}}{{\sin {\rm{A}}}} + \frac{{{{\cos }^3}{\rm{A}} - \cos 3{\rm{\;A}}}}{{\cos {\rm{A}}}}\) we get
(1 – sin A + cos A) 2is equal to
What is \(\frac{{\cos {\rm{\theta }}}}{{1 - \tan {\rm{\theta }}}} + \frac{{\sin {\rm{\theta }}}}{{1 - \cot {\rm{\theta }}}}\) equal to?
