Question

Evaluate sin² 42° - sin² 12°

Answer 1

Greetings , Thanks for the question

It's a question which we can solve by one of trigonometry identities.

We know that,
sin²A - sin²B = sin(A+B) . sin(A-B)

Now,

sin² 42 - sin² 12

= sin ( 42 + 12 ) * sin ( 42 - 12 )

= sin(54) * sin30

$= \frac{1 + \sqrt{5} }{4} \times \frac{1}{2} \\ \\ = \frac{1 + \sqrt{5} }{8}$

Therefore, sin²42 - sin²12 = 1 + √5 / 8

Hope helped! ^^