Question

The value of sin² 51° + sin² 39° is

• A. 1
• B. 0
• C. sin 12°
• D. cos 12°

Answer 1

The Correct Option is A

The value of sin² 51° + sin² 39° is:

We know that \(\sin(90^\circ - x) = \cos(x)\). 

Therefore, \(\sin(51^\circ) = \sin(90^\circ - 39^\circ) = \cos(39^\circ)\).

So, sin² 51° + sin² 39° = cos² 39° + sin² 39°

Using the trigonometric identity \(\sin^2(x) + \cos^2(x) = 1\), we get:

cos² 39° + sin² 39° = 1

Answer: (A) 1

Answer 2

Using the complementary angle identity $ \sin(90^\circ - x) = \cos x $, we have:

$$ \sin^2 51^\circ + \sin^2 39^\circ = \sin^2 51^\circ + \sin^2 (90^\circ - 51^\circ) = \sin^2 51^\circ + \cos^2 51^\circ. $$

Using the Pythagorean identity $ \sin^2 x + \cos^2 x = 1 $, we get:

$$ \sin^2 51^\circ + \cos^2 51^\circ = 1. $$