Question

How do you simplify `cos(pi/2-theta)`?

Answer 1

`sintheta`

Explanation:

This is a well used trig. relation along with `sin(pi/2-theta)`

that is : `cos(pi/2-theta)=sintheta" and " sin(pi/2-theta)=costheta`

Basically sin(angle) = cos(complement)

and cos(angle) = sin(complement)

example: `sin60^@=cos30^@ "etc"`

However, we can show the above question using the appropriate`color(blue)" Addition formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)( cos(A ± B)=cosAcosB ∓ sinAsinB)color(white)(a/a)|)))`

`rArrcos(pi/2-theta)=cos(pi/2)costheta+sin(pi/2)sintheta`

now `cos(pi/2)=0" and " sin(pi/2)=1`

`rArrcos(pi/2-theta)=0xxcostheta+1xxsintheta=sintheta`