Question

Prove that Sina=sin3a/1+2cos2a,then find sin15

Answer 1

Step-by-step explanation:

here is your answer..If you don't want to rationalise it will also be correct but I prefer rationalising. If it helps be kind to mark my answer as brainliest..

Answer 2

$sin15 = \frac{1}{2\sqrt2}$

Step-by-step explanation:

We have to prove that,$sina = \frac{sin3a}{1+2cos2a}$

⇒(sina)(1+2cos2a) = sin3a

By Taking L.H.S.,

sina(1+ cos 2a)

= $sina(1+2(1-2sin^2a))$

= $sina(1+2-4sin^2a)$

=$sina(3-4sin^2a)$

=$3sina-4sin^3a$

= sin3a

=R.H.S.

Now,We have to find,sin15°

By using this formula,

$sina = \frac{sin3a}{1+2cos2a}$

sin(15) = $\frac{sin3.15}{1+2cos2.15}$

        =$\frac{sin45}{1+2cos30}$

        =$\frac{1/\sqrt(2)}{1+2\times\frac{1}{2}}$

      = $\frac{1}{2\sqrt2}$