Question

Evaluate the following :

(sin 72° + cos 18°) (sin 72° − cos 18°)

Answer 1

We have to find: (sin 72° + cos 18°) (sin 72° − cos 18°)

Since `sin(90^@ - theta) = cos theta` So

sin 72° + cos 18°) (sin 72° − cos 18°) = `(sin 72^@)^2 - (cos 18^@)^2`

`= [sin (90^@ - 18^@)]^2 - (cos 18^@)^2`

`= (cos 18^@)^2 - (cos 18^@)^2`

`= cos^2 18^@ - cos^2 18^@`

= 0

So value of `(sin 72^@ + cos 18^@)(sin 72^@ - cos 18^@)` is 0