If -2 -3 -2 then -2-2-2 cos 4 - is equal to

The correct option is D 2sinθ √(2 + √(2(1 + cos4θ))) = √(2 + 2|cos2θ|) = √(2(1 cos2θ)) = 2|sinθ| = 2sinθ as π/2 lt; θ lt; 3π/4 ...

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Parametric Differentiation

If π<2 θ<3 π/...

Question

If $π$ < 2 $θ$ < $\frac{3 π}{2}$ then $\sqrt{2 + \sqrt{2 + 2 c o s 4 θ}}$ is equal to

-2sin $θ$

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-2sin $θ$

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2cos $θ$

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2sin $θ$

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Solution

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\frac{cot (\frac{π}{2} + θ) . sin (- θ) . (cot π - θ)}{cos (2 π - θ) . sin (π + θ) . tan (2 π - θ)} = - csc θ

t a n (π / 4 + θ) + t a n (π / 4 - θ) = a^{2}

t a n^{2} (π / 4 + θ) + t a n^{2} (π / 4 - θ)

5 c o s 2 θ + 2 c o s^{2} θ / 2 + 1 = 0, - π < θ < π

θ

5 cos 2 θ + 2 {cos}^{2} \frac{θ}{2} + 1 = 0, - π < θ < π

θ =

tan (π c o s θ) = cot (π sin θ),

cos (θ - (π / 4)) = \pm (1 / (2 \sqrt{2}))

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