Prove that (1-sinb)/(1+sin2b)=tan^2(45-b) plz the b means beta???

Answer 1

tan 45-b = (tan45-tanb)/(1+tan45 tanb)
= (1-tanb)/(1+tanb)

square that, and you have

(1-2tanb+tan^2b)/(1+2tanb+tan^2b)
= (sec^2b-2tanb)/(sec^2b+2tanb)
= (1/cos^2b - 2sinb/cosb)(1/cos^2b + 2sinb/cosb)
= (1-2sinb cosb)/(1+2sinb cosb)
= (1-sin2b)/(1+sin2b)

I think you have a typo in yours, no?
And why does b have to mean beta? b is just as good.

Answer 2

4cosacosbsinc