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Find the number of real solutions to the...

Find the number of real solutions to the equation `sqrt(1+cos2x)=sqrt2 sin^(-1)(sinx),-pilexlepi`.

A

0

B

1

C

2

D

infinite

Text Solution

Verified by Experts

We have
`sqrt(1+cos 2x)=sqrt(2sin^(-1)(sinx)`
`rarr sqrt(2)|cosx|=sqrt(2)sin^(-1)(sinx)`
`rarr |cos x|=sin^(-1)(sin x)`
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
  1. If [cot^(-1)x]+[cos^(-1)x]=0 , where [] denotes the greatest integer f...

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  2. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

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  3. Find the number of real solutions to the equation sqrt(1+cos2x)=sqrt2 ...

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  4. The number of solution of sin{sin^(-1)(log(1//2)x)}+2|cos{sin^(-1)(x...

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  5. The value of "tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(...

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  6. A value of x satisfying tan(sec^(-1)x)=sin(cos^(-1).(1)/sqrt5) is

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  7. Exhaustive set of values of parameter 'a' so that sin^(-1)x-tan^(-1)x=...

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  8. If a le sin^(-1)x +cos^(-1)x+tan^(-1)x le b, then:

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  9. If -1lexle0 then sin^(-1)x equals

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  10. If tan^(-1) ((x+1)/(x-1))+tan^(-1)((x-1)/x)=tan^(-1)(-7) , then the va...

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  11. Using mathematical induction , prove that tan^(-1)((1)/(3))+tan^(-1)((...

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  12. If -1lexle0 then tan{1/2sin^(-1)(2x)/(1+x^(2))+1/2cos^(-1)(1-x^(2))/...

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  13. If -1lexle0 then tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-x^(2)...

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  14. sin [ tan^(-1). (1 - x^(2))/(2x) + cos^(-1) . (1-x^(2))/(1 + x^(2))] i...

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  15. If -1lexle0 then sin{tan^(-1)((1-x^(2))/(2x))-cos^(-1)((1-x^(2))/(1+x...

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  16. If |cos^-1((1-x^2)/(1+x^2))| < pi/3, then x belongs to the interval

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  17. Find the value of, cos [tan^(-1) {sin (cot^(-1)x)}]

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  18. Find the value of sin^(-1)(cos(sin^(-1)x))+cos^(-1)(sin(cos^(-1)x))

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  19. If (sin^(-1)x)^(2)+(cos^(-1)x)^(2)=(5pi^(2))/(8) then x =

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  20. tan ((pi)/(4) + (1)/(2) cos^(-1) x) + tan ((pi)/(4) - (1)/(2) cos^(-1)...

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