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Let a = cos^(-1) cos 20, b = cos^(-1) co...

Let `a = cos^(-1) cos 20, b = cos^(-1) cos 30 and c = sin^(-1) sin (a + b)` then
If `5 sec^(-1) x + 10 sin^(-1) y = 10 (a + b + c)` then the value of `tan^(-1) x + cos^(-1) (y -1)` is

A

`(pi)/(2)`

B

`(pi)/(4)`

C

`pi`

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`5 sec^(-1) x + 10 sin^(-1) y = 10 pi`
`rArr sec^(-1) x = pi and sin^(-1) y = (pi)/(2)`
`rArr x = - 1, y = 1`
So, `tan^(-1) (-1) + cos^(-1)(0) = -(pi)/(4) + (pi)/(2) = (pi)/(4)`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Comprehension)
  1. For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - s...

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  2. For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - s...

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  3. For x, y, z, t in R, sin^(-1) x + cos^(-1) y + sec^(-1) z ge t^(2) - s...

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  4. If ax + b sec(tan^-1 x) = c and ay + b sec(tan^-ly) = c, then (x+y)/(1...

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  5. If ax + b sec(tan^-1 x) = c and ay + b sec(tan^-ly) = c, then (x+y)/(1...

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  6. If ax + b sec(tan^-1 x) = c and ay + b sec(tan^-ly) = c, then (x+y)/(1...

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  7. Consider the system of equations cos^(-1)x + (sin^(-1) y)^(2) = (p pi^...

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  8. If nin N and the set of equations, (sin^-1 y)^2 + (cos^-1 x)=(n pi^2)/...

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  9. If nin N and the set of equations, (sin^-1 y)^2 + (cos^-1 x)=(n pi^2)/...

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  10. Let cos^(-1) (4x^(3) -3x) = a + b cos^(-1) x If x in [-1, -(1)/(2)),...

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  11. Let cos^-1(4 x^3-3 x)=a+b cos^-1 x . If x in [-1/2,-1], then a+b pi=

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  12. Let cos^(-1) (4x^(3) -3x) = a + b cos^(-1) x If x in ((1)/(2), 1], t...

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  13. Let a = cos^(-1) cos 20, b = cos^(-1) cos 30 and c = sin^(-1) sin (a +...

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  14. Let a = cos^(-1) cos 20, b = cos^(-1) cos 30 and c = sin^(-1) sin (a +...

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  15. Consider the function f(x) = sin^(-1)x, having principal value branch ...

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  16. Consider the function f(x) = sin^(-1)x, having principal value branch ...

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