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Q.

If $α = T a n (\frac{5 π}{16} (\sin (2 \cos^{- 1} \frac{1}{\sqrt{5}})))$ and $β = \cos (\sin^{- 1} (\frac{4}{5}) + \sec^{- 1} (\frac{5}{3}))$ then the inverse trigonometric functions take principal values then the equation whose roots are $α a n d β$ is.

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a

$25 x^{2} + 18 x - 7 = 0$

b

$25 x^{2} + 18 x + 7 = 0$

c

$25 x^{2} - 18 x + 7 = 0$

d

$25 x^{2} - 18 x - 7 = 0$

answer is C.

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Detailed Solution

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$\cos θ = \frac{1}{\sqrt{5}}, \sin θ = \frac{2}{\sqrt{5}}, \sin 2 θ = \frac{4}{5} α = T a n (\frac{5 π}{16} . \frac{4}{5}) = 1 β = \cos (\sin^{- 1} (\frac{4}{5}) + \cos^{- 1} (\frac{3}{5})) = \cos (\cos^{- 1} \frac{3}{5}) + (\cos^{- 1} \frac{3}{5}) = \cos (2 \cos^{- 1} (\frac{3}{5})) β = \frac{- 3}{25}$

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