If cotcos-1x = sectan-1ab2 - a2 :&n

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 Multiple Choice QuestionsMultiple Choice Questions

191.

If 2sinh-1a1 - a2 = log1 + x1 - x, then x is equal to

  • a

  • 1a

  • 1 - a2

  • 11 - a2


192.

If x =sin2tan-12 and y = sin12tan-143, then

  • x > y

  • x = y

  • x = 0 = y

  • x< y


193.

If coshx = 54, then cosh3x = ?

  • 6116

  • 6316

  • 6516

  • 6163


194.

In aABC, if <A = 90°, then cos-1Rr2 +r3 = ?

  • 90°

  • 30°

  • 60°

  • 45°


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195.

If cotcos-1x = sectan-1ab2 - a2 : b > a, then x = 

  • b2b2 - a2

  • b2 - a2ab

  • a2b2 - a2

  • b2 - a2a


A.

b2b2 - a2

a We have, cotcos-1x = sectan-1ab2 - a2 cotcot-1x1 - x2 = secsec-11 + ab2 - a22          cos-1x = cot-1x1 - x2and tan-1x = sec-11 + x2 x1 - x2 = b2 - a2 + a2b2 - a2 x1 - x2 = bb2 - a2On squaring both sides, we getx21 - x2 = b2b2 - a2 x2b2 - x2a2 = b2 - b2x2 x22b2 - a2 = b2 x = b2b2 - a2


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196.

2π - sin-145 + sin-1513 + sin-11665 = ?

  • π2

  • π

  • 3π2

  •  - π2


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