Prove (Sin5A - Sin4A)/(Cos4A + Cos5A) = Tan A/2

Convert all the '5A' and '4A' into simple angles, then half angles.

sin(A+B) = sinAcosB + cosAsinB

sin(2A) = 2sinAcosA

cos(2A) = cos^2A - sin^2A = 2cos^2A - 1 = 1- 2sin^2A

convert all the '5a' and '4a' into simple angles, then half angles.

sin(a+b) = sinacosb + cosasinb

sin(2a) = 2sinacosa

cos(2a) = cos^2a - sin^2a = 2cos^2a - 1 = 1- 2sin^2a

i still don't understand... do u have the solutions?

i still don't understand...do u have the solutions?

cos(A+B)=cosAcosB-sinAsinB

sinC-sinD=2cosC+D/2 . SinC-D/2
cosC+cosD=2cosC+D/2 . CosC-D/2
apply this formula in question i.e
sin5A-sin4A 2cos9A/2 .sinA/2 sinA/2
-------------- = --------------------- = --------- = tanA/2
cos4A+cos5A 2cos9A/2 . CosA/2 cosA/2