cot2(t) / 4 csc(t) = 1 − sin2(t) / 4 sin(t)

Question

Verify the identity by converting the left side into sines and cosines. (Simplify at each step)

Answer 1

cot^2(t)/4csc(t)

= cos^2(t)/sin^2(t)/(4/sin(t)

=cos^2(t)/4sin(t)

=(1-sin^2(t)/4sin(t)

= the right side if you put in some parentheses

but as written, it's not an identity.

plug in t=30 degrees and

both sides are not equal, which proves it's not an identity

cot^2(30)/4csc30 = 3/2sqr3 = sqr3/2

while 1-sin^2(30)/4sin30 = 1-1/8=7/8