Question

if sin0=cos 0 then find the value of sin 0cos 0​

Answer 1

$\star\:\:\:\sf\large\underline\blue{Solution:-}$

Given,

$\sf \sin(x) = \cos(x)$

We have to find the value of

$\sf \sin(x) \cos(x)$

Now, we will solve the problem.

$\sf \sin(x) = \cos(x)$

$\sf \implies \sin(x) - \cos(x) = 0$

Squaring both side, we get,

$\sf \sin^{2} (x) + \cos^{2} (x) - 2 \sin(x) \cos(x) = 0$

Now, we know that,

$\sf { \sin }^{2} (x) + \cos^{2} (x) = 1$

Therefore,

$\sf1 - 2 \sin(x) \cos(x) = 0$

$\sf \implies2 \sin(x) \cos(x) = 1$

$\sf \implies \sin(x) \cos(x) = \frac{1}{2}$

$\star\:\:\:\sf\large\underline\blue{Answer:-}$

• $\sf \implies \sin(x) \cos(x) = \frac{1}{2}$