Question

Which sum or difference identity would you use to verify that sin (90° + q) = cos q?

Answer 1

Most likely cot x = cos x / sin x , but i'm still learning this myself. I hope it helps :)

Answer 2

We are given:

sin(90°+q) = cosq

Let us simplify the left side of equation first,

LHS: sin(90°+q)

Using the property:

$sin(a+b)=sinacosb+sinbcosa$

Let us expand sin(90°+q)

$sin(90+q)=sin(90)cosq+sin(q)cos(90)$

We know that,

sin 90 =1 and cos 90 = 0

Plugging these in the above equation,

$sin(90+q)=(1)cosq+sin(q)(0)$

$sin(90+q)=cosq$

RHS= cos q

Answer: So we can see that option b. sin (a +b) = sin a cos b + cos a sin b is the correct choice.