Question

Evaluate the following:
$1 - 2{\sin ^2}3\theta $ =
A. $\cos ec60$
B. $\tan 60$
C. $\sin 60$
D. $\cos 60$

Answer 1

Hint: In this solution we have to apply the basic double angle formula of cosine.

Complete step-by-step answer:
We know,
$\cos 2\theta = 1 - 2{\sin ^2}\theta $ $\to$ Eq (1)
We can see that the RHS of the above formula is comparable to the given expression in the question, comparing which we get
$\theta = 30^\circ $
So, when we put $\theta = 30^\circ$ in Eq (1) we get,
$\cos 2\left( {30} \right) = 1 - 2{\sin ^2}\left( {30} \right)$ $\to$ Eq (2)
$\therefore$ The answer is $\cos 2\left( {30} \right) = \cos 60$
Therefore the answer is option D. $\cos 60$.

Note: In these types of questions we have to use basic formulas of trigonometry and then put the value of the angle assigned in the question. There is an alternative method as well, where you can solve the expression given, with the help of trigonometric values and then also find the values of the options, the option which has the same value as the question expression is the correct answer.