Question

(1-sin^ 2 theta)(tan theta)=?

Answer 1

Answer:

sin 2theta/2

Step-by-step explanation:

(1-sin^ 2 theta)(tan theta)

Recall in trig identity that

sin^2 theta + cos^2 theta = 1

cos^2 theta = 1-sin^ 2 theta

Also tan theta = sin theta/cos theta

Substitute

(1-sin^ 2 theta)(tan theta)

=cos^2 theta *  sin theta/cos theta

= costheta sin theta

Since sin2 theta = 2sintheta cos theta

sintheta cos theta = sin 2theta/2