If y = tan-1x + sec-1x + cot-1

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 Multiple Choice QuestionsMultiple Choice Questions

31.

In a triangle ABC, the sides b and c are the roots of the equation x2 - 61x + 820 = 0 and A = tan-143, then a2 is equal to

  • 1098

  • 1096

  • 1097

  • 1095


32.

If sin-1x + sin-1y = π2, then cos-1x + cos-1y is equal to :

  • π2

  • π4

  • π

  • 3π4


33.

If tan-1mn - tan-1m - nm +n is equal to

  • tan-1nm

  • tan-1m +nm - n

  • π4

  • tan-112


34.

If sec-11 + x2 + csc-11 +y2y + cot-11z = π, then x + y + z is equal to

  • xyz

  • 2xyz

  • xyz2

  • x2yz


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35.

If tan-1x2 + cot-1x2 = 5π28, then x is equal to

  • 0

  • 2

  • 1

  • - 1


36.

5cos-11 - x21 + x2 + 7sin-12x1 + x2 - 4tan-12x1 + x2 - tan-1x = 5π, then x is equal to

  • 3

  • 3

  • 2

  • 3


37.

If cos-1513 - sin-11213 = cos-1x,  then x is equal to

  • 1

  • 12

  • 0

  • 32


38.

The value of costan-1sincot-1x is

  • x2 + 1x2 - 1

  • 1 - x2x2 + 2

  • 1 - x21 + x2

  • x2 + 1x2 + 2


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39.

If - π2 < sin-1x < π2, then tansin-1x is equal to

  • x1 - x2

  • x1 +x2

  • x1 - x2

  • 11 - x2


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40.

If y = tan-1x + sec-1x + cot-1x + csc-1x, then dydx is equal to

  • x2 - 1x2 + 1

  • π

  • 0

  • 1


C.

0

Given that,

y = tan-1x + sec-1x + cot-1x + csc-1x

Differentiating it w.r.t. x, we get

dydx = 11 + x2 + 1xx2 - 1 - 11 + x2 - 1xx2 - 1      = 0


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