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Solve the equation ( sin x + cos x )^(1+...

Solve the equation `( sin x + cos x )^(1+ sin 2x )=2 ` , when ` -pi le x le pi ` .

A

`(pi)/(2)`

B

`pi`

C

`(pi)/(4)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`("sin" x + "cos" x)^((1+"sin" 2x)) = 2`
`rArr (1+ "sin" 2x)^((1+"sin"2x)) = 2^(2)`
`rArr 1+ "sin" 2x = 2`
`rArr "sin" 2x = 1 rArr 2x = (pi)/(2), - (3pi)/(2)rArr = x = (pi)/(4), -(3pi)/(4)`
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OBJECTIVE RD SHARMA-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
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  11. If the equation "sec" theta + "cosec" theta =c has real roots between ...

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  12. If theta(1), theta(2), theta(3), theta(4) are roots of the equation "s...

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  13. If sin(pi cos theta) = cos(pi sin theta), then of the value cos(th...

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  14. If "tan" (pi "cos" theta) = "cot"(pi "sin" theta), then the value(s) ...

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  15. The general solution of "tan" ((pi)/(2)"sin" theta) ="cot"((pi)/(2)"co...

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  16. The most general value of theta which satisfy both the equation cos th...

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  17. The number of roots of the equation x +2"tan"x = (pi)/(2) in the inter...

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  18. If "sin" (pi "cot" theta) = "cos" (pi "tan" theta), "then cosec" 2 the...

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  19. The number of distinct roots of the equation A"sin"^(3) x + B"cos"^(3...

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  20. The values of x between 0 and 2pi which satisfy the equation sinxsqrt(...

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  21. If Cos20^0=k and Cosx=2k^2-1, then the possible values of x between 0^...

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