Question

solve this trigonometric identity please

Answer 1

this is your answer.

Answer 2

sin(theta) - 2sin^3(theta)/ 2cos^3(thet) - cos(theta)

From the numerator, take sin(theta) common and from denominator cos(theta)

[sin(theta)*(1-2sin^2 theta)]/[cos(theta)*(2cos^2 theta - 1)]

For ''1'' sub sin^2 theta + cos^2 theta
[sin theta* (sin^2 theta + cos^2 theta - 2sin^2 theta)]/[cos theta* (2cos^2 theta - sin^2 theta - cos^2 theta)]
= [sin theta *(cos^2 theta - sin^2 theta)]/[cos theta*(cos^2 theta - sin^2 theta)]
= sin theta/ cos theta = tan theta..... Hence proved.
Hope this helps