Question

Which relationship in the triangle must be true?

sin(B) = sin(A)
sin(B) = cos(90 - B)
cos(B) = sin(180 - B)
COS(B) = COS(A)
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Answer 1

sin(B)=cos(90-B)

Explanation:

sin(B)=cos(90-B) is a co-function identity.

We can also prove it using the difference identity for cosine.

Let's do that:

cos(90-B)

equals

cos(90)cos(B)+sin(90)sin(B)

0cos(B)+1sin(B)

0+sin(B)

sin(B)

Therefore cos(90-B)=sin(B).