Question

How do you prove cos (90 deg + A) = -sin A?

Answer 1

see explanation

Explanation:

using `color(blue)" Addition formula "`

• cos(A ± B ) = cosAcosB ∓ sinAsinB (Note sign change )

applying this to the question to obtain:

`cos(90^@ + A ) = cos90^@cosA - sin90^@sinA`

you should know the following facts:

`cos90^@ = 0 " and " sin90^@ = 1`

`rArrcos(90^@ + A ) = 0xxcosA - 1xxsinA = 0-sinA = -sinA`