Hello! I have been learning about proving identities and can do simple ones but lately I have been really struggling. I am currently stuck on this problem.

Question

cos(A-B)/tan(A)+cot(B) = sin(B)/sec(A)

I managed to get to:
cosAcosB-sinAsinB/(sinA/cosA) + (cosA/sinB) but I am stuck

Answer 1

hint: cos(A-B) = cosAcosB + sinAsinB

tan(A)+cot(B)
= sinA/cosA + cosB/sinB
= (sinAsinB + cosAcosB)/(cosAsinB) , using a common denominator.

now, what happens when you perform the division?

Answer 2

Hello! Thank you for responding, I did some cancelling and now I have

cosAcosB-sinAsinB/sinA+cosB

If I cancel the cosB I end up with

cosA-sinAsinB/sinA

am I allowed to cancel the sinA if the one on top is a negative while the one at the bottom is positive?

Answer 3

Oh sorry I just noticed it is + not -!

Answer 4

I ended up with cosA+sinB :(

Answer 5

LS = (cosAcosB + sinAsinB) / ((sinAsinB + cosAcosB)/(cosAsinB) ), from my first post
= (cosAcosB + sinAsinB)(cosAsinB) / (sinAsinB + cosAcosB)
= cosAsinB
= sinB (1/secA)
= RS