Question

Prove that:- (1-sinA)(1+sinA)÷(1+cosA)(1-cosA)=cot^2A​

Answer 1

see explanation

Explanation:

Using the trigonometric identity

sin²x + cos²x = 1 , then

sin²x = 1 - cos²x and cos²x = 1 - sin²x

Consider the left side

`((1-sinA)(1 + sinA))/((1+cosA)(1-cosA))` ← expand numerator/denominator using FOIL

=
`(1-sin^2A)/(1-cos^2A)`

=
`(1-(1-cos^2A))/(1-(1-sin^2A))`

=
`(1-1+cos^2A)/(1-1+sin^2A)`

=
`(cos^2A)/(sin^2A)`

= cot²A = right side , thus proven