Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Trending Questions

Q. If $si{n}^{-1}\frac{3}{5}+co{s}^{-1}\left(\frac{12}{13}\right)=si{n}^{-1}C,thenC=$

1. $\frac{65}{56}$
2. $\frac{16}{65}$
3. $\frac{56}{65}$
4. $\frac{24}{65}$

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Q. If x < 0, then find the value of
$2\left({\tan }^{-1}\frac{1}{x}+{\tan }^{-1}x\right)$

1. $\pi$
2. $-\pi$
3. $\frac{\pi }{2}$
4. $-\frac{\pi }{2}$

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Q. if $2co{s}^{-1}\sqrt{\frac{1+x}{2}}=\frac{\pi }{2}$, then x=

1. $1$
2. $0$
3. $\frac{-1}{2}$
4. $\frac{1}{2}$

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Q. If $si{n}^{-1}\frac{3}{5}+co{s}^{-1}\left(\frac{12}{13}\right)=si{n}^{-1}C,thenC=$

1. $\frac{65}{56}$
2. $\frac{24}{65}$
3. $\frac{16}{65}$
4. $\frac{56}{65}$

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Q. The value of ${\cos }^{-1}\left(\cos \frac{5\pi }{3}\right)+{\sin }^{-1}\left(\sin \frac{5\pi }{3}\right)$ is

1. $0$
2. $\frac{\pi }{2}$
3. $\frac{2\pi }{3}$
4. $\frac{10\pi }{3}$

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Q. The number of value(s) of $x$ satisfying ${\sin }^{-1}(1-x)-2{\sin }^{-1}x=\frac{\pi }{2}$ is

1. $0$
2. $2$
3. $1$
4. $3$

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Q. If $({\tan }^{-1}x{)}^2+({\cot }^{-1}x{)}^2=\frac{5{\pi }^2}{8},$ then the sum of the solutions in $x$ is

1. $1$
2. $-1$
3. $0$
4. not finite

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Q. The value of x for which $sin\left(co{t}^{-1}\right(1+x\left)\right)=cos\left(ta{n}^{-1}x\right)$ is:

1. $\frac{1}{2}$
2. 1
3. \N
4. $-\frac{1}{2}$

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Q. If x < 0, then find the value of
$2\left({\tan }^{-1}\frac{1}{x}+{\tan }^{-1}x\right)$

1. $\pi$
2. $-\pi$
3. $\frac{\pi }{2}$
4. $-\frac{\pi }{2}$

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Q. Let $x_i,i=1,2,3,\dots ,n$ be the solutions of the equation ${\tan }^{-1}x+{\cot }^{-1}(-\left|x\right|)=2{\tan }^{-1}6x.$ Then $6\sum _{i=1}^n{x}_i$ is equal to

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Q. $tan\left[\frac{1}{2}co{s}^{-1}\left(\frac{\sqrt{5}}{3}\right)\right]=$

1. $\frac{3-\sqrt{5}}{2}$
2. $\frac{3+\sqrt{5}}{2}$
3. $\frac{2}{3-\sqrt{5}}$
4. $\frac{2}{3+\sqrt{5}}$

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