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The number of real solution of the equat...

The number of real solution of the equation `sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi`, is

A

0

B

1

C

2

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
Here `|cos x| = sin^(-1) (sin x)`

From the graph, the number of solutions is 2
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single)
  1. The number of real solution of the equation tan^(-1) sqrt(x^(2) - 3x +...

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  2. If sin^(-1)(x-1)+cos^(-1)(x-3)+tan^(-1)(x/(2-x^2))=cos^(-1)k+pi, then ...

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  3. The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 s...

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  4. The equation 3 cos^(-1) x - pi x - (pi)/(2) =0has

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  5. Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is

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  6. The value of lim(|x| rarr oo) cos (tan^(-1) (sin (tan^(-1) x))) is equ...

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  7. Find the range of tan^(-1)((2x)/(1+x^2))

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  8. Equation [cot^(-1) x] + 2 [tan^(-1) x] = 0, where [.] denotes the grea...

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  9. The number of integral values of k for which the equation sin^(-1)x+ta...

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  10. The range of the values of p for which the equation sin cos^(-1) ( co...

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  11. The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...

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  12. complete solution set of tan^(-1) (sin^(-1) x) gt 1 is

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  13. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  14. The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w ...

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  15. If |cos^(-1) ((1 -x^(2))/(1 + x^(2)))| lt (pi)/(3), then

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  16. The value of sin^(-1) (sin 12) + cos^(-1) (cos 12) is equal to

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  17. The value of the expression sin^(-1)(sin(22pi)/7)cos^(-1)(cos(5pi)/3)+...

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  18. The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x i...

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  19. If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^...

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  20. tan^-1[(cos x)/(1+sin x)] is equal to

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