Using the identity cos^2x + sin^2x = 1, or otherwise, find an equivalent expression to 1+cosx/2sinx + sinx/2+2cosx
If anyone is able to help. Please do.
1+cosx/2sinx + sinx/2+2cosx
If that is
(1 +cosX)/(2sinX) +(sinX)/(2 +2cosX),
then,
Combine the two fractions into one fraction only.
The common denominator is 2(sinX)(1+cosX),
= [(1+cosX)^2 +(sinX)^2] / [2(sinX)(1+cosX)]
= [1 +2cosX +cos^2(X) +sin^2(X)] / [2(sinX)(1+cosX)]
= [1 +2cosX +1] / [2(sinX)(1+cosX)]
= [2 +2cosX] / [(sinX)(2 +2cosX)]
= 1 / sinX
= cscX ------------------answer.