Question

How to do this question? Please tell me the answer with steps

Answer 1

Consider a right angled triangle with hypotenuse c and legs a and b. Let sin theta = a/c .

Then cos theta = b/c and tan (90-theta) = b/a

Then 2 sin theta cos theta / tan (90 - theta)

= 2 * a/c * b/c / b/a

= 2 * ab/c^2 * a/b

= 2 a^2 / c^2 = 2 sin^2 theta

Answer 2

`(2\cos \theta \sin \theta)/(\tan(90-\theta))=2\sin^2 \theta\\\\ (2\cos \theta \sin \theta)/(\cot \theta)=2\sin^2 \theta\\\\ (2\cos \theta \sin \theta)/((\cos \theta)/(\sin \theta))=2\sin^2 \theta\\\\ 2\cos \theta \sin \theta\cdot(\sin \theta)/(\cos \theta)=2\sin^2 \theta\\\\ 2\sin^2 \theta=2\sin^2 \theta`