if-6sin-4-3cos-4-2-then-find-the-value-of-7cosec-6-8sec-6-1-3-

Question Number 24933 by adityapratap2585@gmail.com last updated on 29/Nov/17

if {6 \sin}^{4} θ + {3 \cos}^{4} θ = 2 then find the

value of {({7 cosec}^{6} θ + {8 \sec}^{6} θ)}^{1 / 3}

Commented by prakash jain last updated on 29/Nov/17

\sin^{2} θ = x

6 x^{2} + 3 {(1 - x)}^{2} = 2

6 x^{2} + 3 + 3 x^{2} - 6 x = 2

9 x^{2} - 6 x + 1 = 0

{(3 x - 1)}^{2} = 0 \Rightarrow x = \frac{1}{3} = \sin^{2} θ

{cosec}^{2} θ = 3, \sec^{2} θ = \frac{1}{1 - \sin^{2} θ} = \frac{3}{2}

(7 \times 3^{3} + 8 \times \frac{3^{3}}{2^{2}}) = 27 \times 8 = 216

Commented by adityapratap2585@gmail.com last updated on 29/Nov/17

thanks sir