If \(\cot \theta=\frac{5}{6}\), then the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\) is equal to

Concept -

(a - b)(a + b) = a² - b²

cot θ = cos θ / sin θ  

Explanation -

We have \(\cot θ=\frac{5}{6}\)

Now \(\frac{(1+\sin θ)(1-\sin θ)}{(1+\cos θ)(1-\cos θ)}\)

by using formula we get,

= \(\frac{1- sin^2θ }{1- cos^2 θ }\)

= \(\frac{cos^2θ }{sin^2θ }\)

= cot²θ 

= (5/6)² 

= 25/36

Hence Option (4) is correct.