Question

How do you prove `(1+ cosx)/(sinx + tanx)=(1 + cos2x )/ sin2x`?

Answer 1

Left side: `(1 + cos x)/(sin x + tan x)` =

= `[cos x.(1 + cos x)]/[sin x(1 + cos x)]` =`cos x/sin x = cot x`

Right side: `(1+ cos 2x)/sin^2 x`= `(2cos^2 x)/(2.sin x. cos x)`=

=`cos x/sin x = cot x`

Finally, left side = right side.