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The number of real solutions of the equa...

The number of real solutions of the equation `sqrt(1+cos2x)=sqrt(2)sin^(-1)(sinx),-pilt=xlt=pi` is

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-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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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. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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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. Value of x satisfying tan(sec^(- 1)x)=sin(cos^(- 1)(1/(sqrt(5))))

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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 alpha le sin^(-1)x+cos^(1)x +tan^(-1)xlebeta 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)+pi then x =

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  11. The value of tan^(-1)1/3+tan^(-1)1/7+tan^(-1)1/13+..+tan^(-1)(1)/(n^(...

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  12. If 0lexle1 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. If 0lexle1 then sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^...

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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. The value of cos [tan^-1 {sin (cot^-1 x)}] is

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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)+1/2cos^(-1)alpha}+tan{(pi)/(4)-1/2cos^(-1)alpha} alpha ...

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