If 15 sin 4 + 10 cos 4 = 6 , for R , then the value of 27 sec 6 + 8 c o s e c 6 is equal to:

Question

If $15 \sin^{4} α + 10 \cos^{4} α = 6$ , for $α \in R$ , then the value of $27 \sec^{6} α + 8 c o s e c^{6} α$ is equal to:

Smart Achievers · Accepted Answer

(2)

$15 \sin^{4} α + 10 {(1 - \sin^{2} α)}^{2} = 6.25 \sin^{4} α - 20 \sin^{2} α + 4 = 0$

$\Rightarrow 25 \sin^{4} α - 10 \sin^{2} α - 10 \sin^{2} α + 4 = 0$

$\Rightarrow (5 \sin^{2} α - 2) = 0$

$\Rightarrow \sin^{2} α = \frac{2}{5}$

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