Question

2 Sin 75 degree × sin 15 degree = 1 by 2​

Answer 1

Answer:

LHS.=

2sin 75 degree= 2× sin(90-15)= 2×cos15 degree

then according to question - 2cos 15 degree × sin 15 degree = 2cos 30 degree

(formula-- cos2a= 2cosa sina)

then

cos 30degree= 1/2

=RHS

Answer 2

$2\sin 75 \times \sin 15=\dfrac{1}{2}$, proved.

Step-by-step explanation:

To prove that, $2\sin 75 \times \sin 15=\dfrac{1}{2}$.

L.H.S. = $2\sin 75 \times \sin 15$

$=2\sin 75 \times \sin (90-75)$

Using the trigonometric identity,

$\cos A=\sin (90-A)$

$=2\sin 75 \times \cos 75$

Using the trigonometric identity,

$\sin 2A=2\sin A \times \cos A$

$= \sin 2\times 75$

= $\sin 150$

$=\sin (180-30)$

Using the trigonometric identity,

$\sin A=\sin (180-A)$

$=\sin (180-30)$

$=\sin 30$

= $\dfrac{1}{2}$

= R.H.S., proved.

Thus, $2\sin 75 \times \sin 15=\dfrac{1}{2}$, proved.