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If tan^(-1)(sin^2theta-2sintheta+3)+cot^...

If `tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2,` then value of `cos^2theta-sintheta` is equal to

A

0

B

`-1`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
From the given equation `sin^(2) theta - 2 sin theta + 3 = 5^("sec"^(2)y) + 1`, we get
`(sin theta -1)^(2) + 2 = 5^("sec^(2)y) + 1`
`L.H.S. le 6, R.H.S. ge 6`
Possible solution is `sin theta = -1` when L.H.S. = R.HgtS.
`rArr cos^(2) theta = 0`
`rArr cos^(2) theta - sin theta = 1`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single)
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  9. theta = tan^(-1) (2 tan^(2) theta) - tan^(-1) ((1)/(3) tan theta) " th...

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  10. If y = tan^(-1).(1)/(2) + tan^(-1) b, (0 b lt 1) and 0 lt y le (pi)/(4...

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  11. If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1...

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  12. The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...

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  14. Arithmetic mean of the non-zero solutions of the equation tan^-1 (1/(2...

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  15. If cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1, then x+y...

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  16. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

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  17. The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(...

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  18. if cot^(-1)[sqrt(cosalpha)]-tan^(-1)[sqrt(cosalpha)]=x then sinx is eq...

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  19. sum(r =1)^(n) sin^(-1) ((sqrtr - sqrt(r -1))/(sqrtr(r + 1))) is equal...

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