Question

Prove the following equation: sin ( 90 + theta ) = cos theta . .

Answer 1

To prove this kind of equation you must use the Trigonometric Function of Equality. And came up with the formula of sin(x+y) = sin(x)*cos(y)+cos(x)*sin(y) and then substitute the variables that is present if your function and came up with an answer of sin(90-theta)=sin(90)*cos(theta)+cos(90)*sin(theta)=cos(theta)
I hope i answered your question

Answer 2

using the trigonometric equality:

sin(x+y)=sin(x)*cos(y)+cos(x)*sin(y)

then:

sin(90+θ)=sin(90)*cos(θ)+cos(90)*sin(θ)=cos(θ)