If x -1-0- then cos -12 x 2-1-2 sin -1 x is equal toA- - B- -2C- 3 -2D- -2 -

The correct option is A πWhen x lt;0, cos^ 1(2x^2 1)=2π 2cos^ 1x ∴ cos^ 1(2x^2 1) 2sin^ 1x=2π 2cos^ 1x 2sin^ 1x =2π 2(cos^ 1x+sin^ 1x) =2π 2×π/2=π ...

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Byju's Answer

Standard XII

Mathematics

Many-One onto Function

If x ϵ[-1,0],...

Question

If $x ϵ [- 1, 0]$ , then $c o s^{- 1} (2 x^{2} - 1) - 2 s i n^{- 1} x$ is equal to

- \frac{π}{2}

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π

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\frac{3 π}{2}

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- 2 π

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Solution

The correct option is B $π$
When $x < 0, c o s^{- 1} (2 x^{2} - 1) = 2 π - 2 c o s^{- 1} x ∴ c o s^{- 1} (2 x^{2} - 1) - 2 s i n^{- 1} x = 2 π - 2 c o s^{- 1} x - 2 s i n^{- 1} x = 2 π - 2 (c o s^{- 1} x + s i n^{- 1} x) = 2 π - 2 \times \frac{π}{2} = π$

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If xϵ[−1,0], then cos−1(2x2−1)−2sin−1x is equal to

The correct option is B πWhen x<0,cos−1(2x2−1)=2π−2cos−1x∴ cos−1(2x2−1)−2sin−1x=2π−2cos−1x−2sin−1x=2π−2(cos−1x+sin−1x)=2π−2×π2=π

If $x ϵ [- 1, 0]$ , then $c o s^{- 1} (2 x^{2} - 1) - 2 s i n^{- 1} x$ is equal to

The correct option is B $π$
When $x < 0, c o s^{- 1} (2 x^{2} - 1) = 2 π - 2 c o s^{- 1} x ∴ c o s^{- 1} (2 x^{2} - 1) - 2 s i n^{- 1} x = 2 π - 2 c o s^{- 1} x - 2 s i n^{- 1} x = 2 π - 2 (c o s^{- 1} x + s i n^{- 1} x) = 2 π - 2 \times \frac{π}{2} = π$