Question

prove sin75*=[√6+2]/4

Answer 1

hello dear...

your answer is in the attachment.

hope it helps...

Answer 2

Answer and explanation:

To prove : $\sin 75=\frac{\sqrt6+2}{4}$

Proof :

Taking LHS,

$LHS=\sin 75$

$LHS=\sin (30+45)$

Using identity, $\sin(A+B)=\sin A\cos B+\cos A\sin B$

$LHS=\sin 30\cos 45+\cos 30\sin 45$

Substitute the trigonometric values,

$LHS=\frac{1}{2}\times \frac{1}{\sqrt2}+\frac{\sqrt3}{2}\times \frac{1}{\sqrt2}$

$LHS=\frac{1}{2\sqrt2}+\frac{\sqrt3}{2\sqrt2}$

$LHS=\frac{1+\sqrt3}{2\sqrt2}$

Multiply and divide by $\sqrt{2}$

$LHS=\frac{1+\sqrt3}{2\sqrt2}\times \frac{\sqrt2}{\sqrt2}$

$LHS=\frac{\sqrt2+\sqrt6}{2\times 2}$

$LHS=\frac{\sqrt2+\sqrt6}{4}$

$LHS=RHS$

Hence proved.