Question

sin^2(24)- sin^2(6) =...?

Answer 1

We have, sin²A-sin²B=sin(A+B)sin(A-B) hence, sin²24-sin²6=sin30sin18=(1/2)(√5-1)/4=(√5-1)/8 Answer: (√5-1)/8

Answer 2

Answer:

$\sin^2(24)-\sin^2(6)= \frac{\sqrt5-1}{8}$

Step-by-step explanation:

Given : Expression $\sin^2(24)-\sin^2(6)$

To find : The value of the expression ?

Solution :

Using trigonometric identity,

$\sin^2A - \sin^2B = \sin(A-B)\sin(A+B)$

Where, A=24 and B=6

Substitute in the formula,

$\sin^2(24)-\sin^2(6)= \sin(24-6)\sin(24+6)$

$\sin^2(24)-\sin^2(6)= \sin(18)\sin(30)$

$\sin^2(24)-\sin^2(6)= \sin(18)\times \frac{1}{2}$

We know, $\sin(18)=\frac{\sqrt5-1}{4}$

$\sin^2(24)-\sin^2(6)= \frac{\sqrt5-1}{4}\times \frac{1}{2}$

$\sin^2(24)-\sin^2(6)= \frac{\sqrt5-1}{8}$

Therefore, $\sin^2(24)-\sin^2(6)= \frac{\sqrt5-1}{8}$