Question

What is the answer of $\sin \theta . \cos \theta$?

Answer 1

Hint: As we know that the above question is related to trigonometry. And sine, cosine are trigonometric ratios. These are the basic trigonometric functions. In this question we can solve it by applying the trigonometric identities . We know that formulas which represent trigonometric functions of an angle $ 2\theta $ in the form of trigonometric functions of an angle $ \theta $ , are known as double angle formulas.

Complete step by step solution:
According to the question we have to find the value of $ \sin \theta \cos \theta $ .
We know the double angle formula of sine i.e.
 $ \sin 2\theta = 2\sin \theta \cos \theta $ .
By dividing the both left and right hand side of the equation by $ 2 $ , we have:
 $ \dfrac{{\sin 2\theta }}{2} = \dfrac{{2\sin \theta \cos \theta }}{2} $ .
It gives us the value, $ $ $ \sin \theta \cos \theta = \dfrac{1}{2}\sin 2\theta $ .
Hence the required answer is $ \sin \theta \cos \theta = \dfrac{1}{2}\sin 2\theta $ .
So, the correct answer is “$\dfrac{1}{2}\sin 2\theta $”.

Note: Before solving this kind of question we should have the proper knowledge of trigonometric functions, identities and formulas. We should apply the correct trigonometric property to solve the question. The double angle formula of cosine function is $ \cos 2\theta = {\cos ^2}\theta - {\sin ^2}\theta $.