Question

verify identity (1+cos^2 3t) / sin^2 3t) = 2 csc^2 3t -1

Answer 1

\[ \frac{ 1+\cos ^{2}3 \theta }{ \sin ^{2} 3 \theta } = 2 \csc ^{2} 3\theta -1\]

Answer 2

You can separate the fraction: \[\frac{ 1 }{ \sin^2(3 \theta) } + \frac{ \cos^2(3 \theta) }{ \sin^2(3 \theta) } = \csc^2(3 \theta)+[\frac{ 1+\sin^2(3 \theta) }{ \sin^2(3 \theta) }]=\]
now, continuting, you can seaprate even further: \[\csc^2(3 \theta)+[\frac{ 1 }{ \sin^2(3 \theta) }+\frac{ \sin^2 (3 \theta) }{ \sin^2(3 \theta) }] = \]

You should be able to recognize trig functions and finish the problem off. I already did most of the proof. So...yeah. Bye.

Answer 3

@abb0t, that should be a minus sign on the third term.

Answer 4

There, siths provided even more help!