If c o s 6 α + s i n 6 α + K s i n 2 2 α = 1 , then K= Options: A . &nbsp 4 3 B . &nbsp 3 4 C . &nbsp 1 2 D . &nbsp 2

If cos6α+sin6α+K sin22α=1, then K=

Discussion Forum : Trigonometric Functions

Question -

If $c o s^{6} α + s i n^{6} α + K s i n^{2} 2 α = 1$ , then K=

Options:

A .

\frac{4}{3}

B .

\frac{3}{4}

C .

\frac{1}{2}

D . 2

Answer: Option B
:
B

Since $c o s^{6} α + s i n^{6} α + K s i n^{2} 2 α = 1$ using formula $a^{3} + b^{3} = (a + b)^{3} - 3 a b (a + b)$ and on solving, we get the required result i.e., $K = \frac{3}{4}$

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