Question

if tana=1 than prove that 2sina.cosa=1

Answer 1

$2\sin A.\cos A$ = 1, proved.

Step-by-step explanation:

We have,

$\tan A$ = 1

Prove that, $2\sin A.\cos A$ = 1

∴ $\tan A$ = 1

Using the trigonometric identity,

$\tan 45$ = 1

On comparing both sides, we get

⇒ A = 45°

L.H.S. = $2\sin A.\cos A$

Put A = 45°, we get

= $2\sin 45.\cos 45$

We know that,

The trigonometric identity,

$\sin 45=\dfrac{1}{\sqrt{2}}$ and

$\cos 45=\dfrac{1}{\sqrt{2}}$

$=2(\dfrac{1}{\sqrt{2}}).(\dfrac{1}{\sqrt{2}})$

$=2\times \dfrac{1}{2}$

= 1 = R.H.S., proved.

Thus, $2\sin A.\cos A$ = 1, proved.