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

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

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)