Please explain Simplify each of the trigonometric expression

Simplify each of the trigonometric expressions. a) (1 + sin x)(1-sin x) b) tan^4 x - 1/tan^2 x - 1

Solution

a) (1+sin x)(1-sin x)

=(1-sin^2 x)

We know that 1-sin ^2(x) = cos^2 (x)

Therefore (1+sinx )(1-sin x) = cos ^2 x.

b) ( tan ^4 x-1)/(tan ^2 x -1)

We can write tan ^4x -1 =( tan ^x -1)(tan ^x + 1)

Therefore tan ^2 x +1

= sec ^2 x. Ans