Mathematics - Inverse Circular Functions

Question - 1

$x\epsilon\left({3\pi\over 2}, 2\pi\right)$then the value of the expression sin-1 [cos {cos-1 (cos x)} + sin-1 (sin x)], is

• A $-{\pi\over 2}$
• B ${\pi\over 2}$
• C 0
• D $\pi$

Question - 2

The sum of the infinite terms of the series $tan^{-1}\left(1\over 3\right)+tan^{-1}\left(2\over 9\right)+tan^{-1}\left(4\over 33\right)+......$ is equal to

• A $\pi\over 6$
• B $\pi\over 4$
• C $\pi\over 3$
• D $\pi\over 2$

Question - 3

If $sin^{-1}\sqrt{(x^2+2x+1)}+sec^{c-1}\sqrt{(x^2+2x+1)}={\pi\over 2}$x ≠ 0, then the value of $2sec^{-1}\left(x\over 2\right)+sin^{-1}\left(x\over 2\right)$ is equal to

• A $-{3\pi\over 2}$
• B ${3\pi\over 2}$
• C $-{\pi\over 2}$
• D ${\pi\over 2}$

Question - 4

The greatest of tan1, tan-1 1, sin-11, sin1, cos 1, is

• A sin 1
• B tan 1
• C tan-1 1
• D none of these

Question - 5

The value of 'a' for which a x2 + sin-1 (x2 - 2x + 2) + cos-1 (x2 - 2x + 2) = 0 has a real solution, is

• A $-{2\over\pi}$
• B ${2\over\pi}$
• C $-{\pi\over2}$
• D ${\pi\over2}$

Question - 6

If $sin^{-1}x+sin^{-1}y+sin^{-1}z={3\pi\over 2}$ and f(1)=2 f(p + q) = f(p)· f(q), p, q ∈ R, $X^{f(1)} + y^{f(2)} + z^{f(3)}-{(x+y+z)\over X^{f(1)} + y^{f(2)} + z^{f(3)}}$

• A 0
• B 1
• C 2
• D 3

Question - 7

If the mapping f(x)=ax+b,a>0 maps [-1,1] onto [0, 2], then cot [cot-1 7 + cot-1 8 + cot-1 18] is equal to

• A f( - 1)
• B f(0)
• C f(1)
• D f(2)

Question - 8

The sum of the infinite series $sin^{-1}\left(1\over \sqrt2\right)+sin^{-1}\left(\sqrt2-1\over \sqrt6\right)+sin^{-1}\left(\sqrt3-\sqrt2\over \sqrt{12}\right)+.......+........+sin^{-1}\left(\sqrt n-\sqrt{(n-1)}\over \sqrt\{n(n+1)\}\right)+.........$is

• A $\pi\over 8$
• B $\pi\over 4$
• C $\pi\over 2$
• D $\pi$

Question - 9

If [sin-1 cos-1 sin-1 tan-1 x] = 1, where [.] denotes the greatest integer function, then x belongs to the interval

• A [tan sin cos 1, tan sin cos sin 1]
• B (tan sin cos 1, tan sin cos sin 1)
• C [- 1, 1]
• D [sin cos tan 1, sin cos sin tan 1]

Question - 10

If [cot-1x]+ [cos-1 x] = 0, where x is a non-negative real number and [.] denotes the greatest integer function, then complete set of values of x is

• A (cos 1,1]
• B (cot 1,1)
• C (cos 1, cot 1)
• D none of these