If 10 sin^4 alpha + 15 cos^4 alpha = 6,then 1 | vedclass

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(C) Given: $10 \sin^4 \alpha + 15 \cos^4 \alpha = 6$ Divide by $\cos^4 \alpha$: $10 	an^4 \alpha + 15 = 6 \sec^4 \alpha$ $10 	an^4 \alpha + 15 = 6(1

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$62$

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(C) Given: $10 \sin^4 \alpha + 15 \cos^4 \alpha = 6$ Divide by $\cos^4 \alpha$: $10 	an^4 \alpha + 15 = 6 \sec^4 \alpha$ $10 	an^4 \alpha + 15 = 6(1 + 	an^2 \alpha)^2$ $10 	an^4 \alpha + 15 = 6(1 + 2 	an^2 \alpha + 	an^4 \alpha)$ $10 	an^4 \alpha + 15 = 6 + 12 	an^2 \alpha + 6 	an^4 \alpha$ $4 	an^4 \alpha - 12 	an^2 \alpha + 9 = 0$ $(2 	an^2 \alpha - 3)^2 = 0$ $	an^2 \alpha = \frac{3}{2}$ Then,$\cot^2 \alpha = \frac{2}{3}$ Now,$16 	an^6 \alpha + 27 \cot^6 \alpha = 16(\frac{3}{2})^3 + 27(\frac{2}{3})^3$ $= 16(\frac{27}{8}) + 27(\frac{8}{27}) = 54 + 8 = 62$

If $10 \sin^4 \alpha + 15 \cos^4 \alpha = 6$,then $16 \tan^6 \alpha + 27 \cot^6 \alpha =$

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