Question

13. If sin ß is the G.M. between sina and coso then cos2ß A) 2sin² 4 B) 2 cos² 4 C) 2 cos² + 4 2 D) 2 sin² + α 4​

Answer 1

If sinβ is the geometric mean between sinα and cosα, then sin² β=sinα.cosα

⇒cos2β=1−2sin² β

=1−2sinα.cosα

⇒cos²2β=(1−sin2α)²

Now if we simplify option A using 2sinA.cosB=sin(A+B)+sin(A−B), we get

$2 \sin {}^{2} ( \frac{\pi}{4} - a ) 2 \cos {}^{2} ( \frac{\pi}{4} + a )$

$(2 \sin ( \frac{\pi}{4} - a ) \cos ( \frac{\pi}{4} + a ) {)}^{2}$

$\small= ( \sin\frac{\pi}{4} \sin(−2α)) {}^{2} = (1− \sin2α)$