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