If ^6 + ^6 + K , ^2 2 = 1, then K = - Vidyadip

MCQ

If ${\cos ^6}\alpha + {\sin ^6}\alpha + K\,{\sin ^2}2\alpha = 1,$ then $K =$

A
$\frac{4}{3}$
✓
$\frac{3}{4}$
C
$\frac{1}{2}$
D
$2$

✓

Answer

Correct option: B.

$\frac{3}{4}$

b
(b) Since ${\cos ^6}\alpha + {\sin ^6}\alpha + K{\sin ^2}2\alpha = 1$

using formula ${a^3} + {b^3} = {(a + b)^3} - 3ab(a + b)$ and on solving,

we get the required result $i.e.$ $K = \frac{3}{4}$.

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