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The number of solutions of "cos"(2sin^(-...

The number of solutions of `"cos"(2sin^(-1)("cot"(tan^(-1)(sec(6cos e c^(-1)x))))+1=0` where `x >0` is

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The correct Answer is:
3
`cos (2 sin^(-1) (cot (tan^(-1) (sec(6 cosec^(-1) x))))) = -1`
`rArr sin^(-1) (cot (tan^(-1) (sec (6 cosec^(-1) x)))) = +- (pi)/(2)`
`rArr cot (tan^(-1) (sec(6 cosec^(-1) x))) = +-1`
`rArr tan^(-1) (sec(6 cosec^(-1) x)) = (pi)/(4), (3pi)/(4)`
`rArr sec(6 cosec^(-1) x) = +-1`
`rArr 6 cosec^(-1) x = +- 3pi, 2pi, +- pi`
`rArr cosec^(-1) x = +- (pi)/(2), +- (pi)/(3), +- (pi)/(6)`
`rArr x = 1, (2)/(sqrt3) , 2 " " ( :' x gt 0)`
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Numerical value type
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  15. Number of solutions of equation sin(cos^(-1)(tan(sec^(-1)x)))=sqrt(1+x...

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  16. If the equation sin^(-1)(x^2+x+1)+cos^(-1)(lambda x+1)=pi/2 has exactl...

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  17. sin{2(sin^(-1)(sqrt(5))/3-cos^(-1)(sqrt(5))/3)} is equal to (ksqrt(5)...

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  18. The number of solutions of "cos"(2sin^(-1)("cot"(tan^(-1)(sec(6cos e c...

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