Question

Verify the following equalities:

cos 90° = 1 – 2sin² 45° = 2cos² 45° – 1

Answer 1

cos 90° = 0, sin 45° = `1/sqrt(2)`, cos 45° = `1/sqrt(2)`

cos 90° = 0  ...(1)

1 – 2 sin² 45° = `1 - 2(1/sqrt(2))^2`

= `1 - 2 xx 1/2`

= 1 – 1 = 0 → (2)

2 cos² 45° – 1 = `2(1/sqrt(2))^2 - 1`

= `2/2 - 1`

= `(2 - 2)/2`

= 0 → (3)

From (1), (2) and (3) we get

cos 90° = 1 – 2 sin² 45° = 2 cos² 45° – 1

Hence it is proved.