JEE Main Mathematics - Inverse Trigonometric Functions
Exam Duration: 60 Mins Total Questions : 30
If \({ tan }^{ -1 }x=\frac { \pi }{ 10 } \) for some \(x\epsilon R\), then the value of cot-1 x is
- (a)
\(\frac { \pi }{ 5 } \)
- (b)
\(\frac { 2\pi }{ 5 } \)
- (c)
\(\frac { 3\pi }{ 5 } \)
- (d)
\(\frac { 4\pi }{ 5 } \)
\({ tan }^{ -1 }\sqrt { 3 } -{ cot }^{ -1 }(-\sqrt { 3 } )\) is equal to
- (a)
\(\pi \)
- (b)
\(-\frac { \pi }{ 2 } \)
- (c)
zero
- (d)
\(2\sqrt { 3 } \)
The value of cos (2cos-1 x + sin-1 x) at \(x=\frac { 1 }{ 5 } \) is
- (a)
1
- (b)
3
- (c)
0
- (d)
\(-\frac { 2\sqrt { 6 } }{ 5 } \)
If the value of \({ sin }^{ -1 }\frac { 8 }{ 17 } +{ sin }^{ -1 }\frac { 3 }{ 5 } \) is tan-1 x, then x is
- (a)
\(\frac { 77 }{ 35 } \)
- (b)
\(\frac { 77 }{ 36 } \)
- (c)
\(\frac { 77 }{ 37 } \)
- (d)
\(\frac { 77 }{ 26 } \)
If \(f(x)={ e }^{ { cos }^{ -1 }sin\left( x+\frac { \pi }{ 3 } \right) }\), then
- (a)
\(f\left( -\frac { 7\pi }{ 4 } \right) ={ e }^{ \frac { \pi }{ 11 } }\)
- (b)
\(f\left( \frac { 8\pi }{ 9 } \right) ={ e }^{ \frac { 13\pi }{ 18 } }\)
- (c)
\(f\left( -\frac { 7\pi }{ 4 } \right) ={ e }^{ \frac { 3\pi }{ 12 } }\)
- (d)
\(f\left( -\frac { 7\pi }{ 4 } \right) ={ e }^{ \frac { 11\pi }{ 13 } }\)
If \({ sin }^{ -1 }\left( \frac { x }{ 5 } \right) +{ cosec }^{ -1 }\left( \frac { 5 }{ 4 } \right) =\frac { \pi }{ 2 } \), then the value of x is
- (a)
1
- (b)
3
- (c)
4
- (d)
5
If \({ cos }^{ -1 }x-{ cos }^{ -1 }\frac { y }{ 2 } =\alpha ,\)then 4x2 - 4xy cos \(\alpha\) + y2 is equal to
- (a)
\(-4{ sin }^{ 2 }\alpha \)
- (b)
\(4{ sin }^{ 2 }\alpha \)
- (c)
4
- (d)
\(2sin2\alpha \)
Find the principal values of \(sin^{-1}(\frac{-1}{2})\)
- (a)
\(\frac{\pi}{3}\)
- (b)
\(-\frac{\pi}{3}\)
- (c)
\(\frac{\pi}{6}\)
- (d)
\(-\frac{\pi}{6}\)
Find the principal values of \(cos^{-1}(\frac{1}{2})\)
- (a)
\(-\frac{\pi}{3}\)
- (b)
\(\frac{\pi}{3}\)
- (c)
\(\frac{\pi}{2}\)
- (d)
\(\frac{2\pi}{3}\)
Find the principal values of \(cosec^{-1}(\frac{-2}{\sqrt{3}})\)
- (a)
\(-\frac{\pi}{3}\)
- (b)
\(\frac{\pi}{3}\)
- (c)
\(\frac{\pi}{2}\)
- (d)
\(-\frac{\pi}{2}\)
Find the principal values of cot-1(1)
- (a)
\(\frac{\pi}{3}\)
- (b)
\(\frac{\pi}{4}\)
- (c)
\(\frac{\pi}{2}\)
- (d)
0
Find the principal values of \(sin^{-1}(\frac{1}{\sqrt{2}})\)
- (a)
\(\frac{\pi}{4}\)
- (b)
\(\frac{\pi}{3}\)
- (c)
\(\frac{\pi}{6}\)
- (d)
\(\frac{\pi}{2}\)
Find the principal values of \(tan^{-1}(-\sqrt{3})+sec^{-1}(-2)-cosec^{-1}(\frac{2}{\sqrt{3}})\)
- (a)
\(\frac{5\pi}{6}\)
- (b)
\(\frac{2\pi}{3}\)
- (c)
\(\frac{\pi}{3}\)
- (d)
0
Range of f(x)=sin-1x+tan-1x+sec-1x is
- (a)
\((\frac{\pi}{4},\frac{3\pi}{4})\)
- (b)
\([\frac{\pi}{4},\frac{3\pi}{4}]\)
- (c)
\(\{\frac{\pi}{4},\frac{3\pi}{4}\}\)
- (d)
None of these
4 tan-1\(\frac{1}{5}\)-tan-1\(1\over70\)+tan-1\(1\over99\) is equal to
- (a)
\(\pi/6\)
- (b)
\(\pi/4\)
- (c)
\(\pi/3\)
- (d)
\(\pi/2\)
If 2sin-1x=sin-1(2x\(\sqrt{1-x^2}\)), then x belongs to
- (a)
[-1,1]
- (b)
\([-\frac{1}{\sqrt{2}},1]\)
- (c)
\([-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}]\)
- (d)
None of these
\({ cos }^{ -1 }[cos(2{ cot }^{ -1 }(\sqrt { 2 } -1))]\)=
- (a)
\(\sqrt{2}-1\)
- (b)
1+\(\sqrt{2}\)
- (c)
\(\frac{\pi}{4}\)
- (d)
\(\frac{3\pi}{4}\)
\({ tan }\left( \frac { \pi }{ 4 } +\frac { 1 }{ 2 } { cos }^{ -1 }x \right) +tan\left( \frac { \pi }{ 4 } -\frac { 1 }{ 2 } { cos }^{ -1 }x \right) =\)
- (a)
x
- (b)
\(\frac{1}{x}\)
- (c)
2x
- (d)
\(\frac{2}{x}\)
If 2sin-1x-3cos-1x=4, then 2sin-1x+3cos-1x is equal to
- (a)
\(\frac{6\pi-4}{5}\)
- (b)
\(\frac{4-6\pi}{5}\)
- (c)
\(\frac{3\pi}{2}\)
- (d)
0
If m and M are the least and the greatest values of (cos-1x)2+(sin-1x) 2 , then \(\frac{M}{m}=\)
- (a)
10
- (b)
5
- (c)
4
- (d)
2
Solve the following equation sin-1(1-x)-2sin-1x=\(\frac{\pi}{2}\)
- (a)
0
- (b)
1/2
- (c)
0,1/2
- (d)
-1/2
The domain of the function cos-1(2x-1) is
- (a)
[0,1]
- (b)
[-1,1]
- (c)
(-1,1)
- (d)
[0,π]
The domain of the function defined by f(x)=sin-1\(\sqrt{x-1}\) is
- (a)
[1,2]
- (b)
[-1,1]
- (c)
[0,1]
- (d)
none of these
If cos\((sin^{-1}\frac{2}{5}+cos^{-1}x)=0\), then x is equal to
- (a)
\(1\over5\)
- (b)
\(2\over5\)
- (c)
0
- (d)
1
The value of expression 2sec-1 2+sin-1\((\frac{1}{2})\) is
- (a)
\(\frac{\pi}{6}\)
- (b)
\(\frac{5\pi}{6}\)
- (c)
\(\frac{7\pi}{6}\)
- (d)
1
If \(sin^{-1}(\frac{2a}{1+a^2})+cos^{-1}(\frac{1-a^2}{1+a^2})=tan^{-1}(\frac{2x}{1-x^2})\) , where a, x ∈ ]0,1[, then the value of x is
- (a)
0
- (b)
\(\frac{a}{2}\)
- (c)
a
- (d)
\(\frac{2a}{1-a^2}\)
The value of \(cot[cos^{-1}(\frac{7}{25})]\) is
- (a)
\(\frac{25}{24}\)
- (b)
\(\frac{25}{7}\)
- (c)
\(\frac{24}{25}\)
- (d)
\(\frac{7}{24}\)
\(\frac{\alpha^3}{2}cosec^2(\frac{1}{2}tan^{-1}\frac{\alpha}{\beta})+\frac{\beta^3}{2}sec^2(\frac{1}{2}tan^{-1}\frac{\beta}{\alpha})=\)
- (a)
\((\alpha+\beta)(\alpha^2+\beta^2)\)
- (b)
\((\alpha-\beta)(\alpha^2-\beta^2)\)
- (c)
\(\alpha+\beta\)
- (d)
\(\alpha^2+\beta^2\)
Statement I: If 2(sin-1 x)2-5(sin-1x)+2=0, then x has 2 solutions.
Statement II: sin-1(sin x)=x, if \(-\frac{\pi}{2}\le x\le \frac{\pi}{2}\)
- (a)
If both statement I and statement II are true and statement II is the correct explanation of statement I
- (b)
If both statement I and statement II are true but statement II is not the correct explanation of statement I
- (c)
If statement I is true but statement II is false.
- (d)
If statement I is false and statement II is true.