State true or false.
$cos 2 x = {cos}^{2} x - {sin}^{2} x$

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
As we know that
$cos (A + B) = cos A cos B - sin A sin B$
So $cos 2 x = cos (x + x) = cos x \times cos x - sin x \times sin x = {cos}^{2} x - {sin}^{2} x$
So the relation is $True$

Suggest Corrections

Similar questions

\frac{sin x + sin 2 x}{1 + cos x + cos 2 x} = tan x

- 4 \leq c o s 2 x + 3 s i n x \leq \frac{17}{8}

\int \frac{(p^{x} + q^{x})^{2}}{p^{x} . q^{x}} + \frac{e^{5 l o g_{e} x} - e^{4 l o g_{e} x}}{e^{3 l o g_{e} x} - e^{2 l o g_{e} x}} + \frac{{sin}^{2} x + {cos}^{2} x}{{sin}^{2} x {cos}^{2} x} d x

= \frac{(p / q)^{x}}{l o g (p / q)} + \frac{(q / p)^{x}}{l o g (q / p)} + 2 x + \frac{x^{3}}{3} + tan x - cot x

\frac{1 + sin 2 x + cos 2 x}{1 + sin 2 x - cos 2 x} = cot x

Let $f (x) = s i n^{2} x + c o s^{2} x, g (x) = 1$

f(x) and g(x) are identical

Join BYJU'S Learning Program