Properties with Negative X

Q.

Solve:

$\frac{\left(cotA-1\right)}{\left(2-se{c}^{2}A\right)}=\frac{\left(cotA\right)}{\left(1+\tan A\right)}$

Q. Let $f\left(x\right)=x{\cos }^{-1}\left(\sin \right(-|x|\left)\right),x\in (-\frac{\pi }{2},\frac{\pi }{2})$, then which of the following is true ?

1. $f^{\prime }\left(0\right)=-\frac{\pi }{2}$
2. $f^{\prime }$ is decreasing in $(-\frac{\pi }{2},0)$ and increasing in $(0,\frac{\pi }{2})$
3. $f$ is not differentiable at $x=0$
4. $f^{\prime }$ is increasing in $(-\frac{\pi }{2},0)$ and decreasing in $(0,\frac{\pi }{2})$

Q.

Find the value of the trigonometric function

Q.

Evaluate ${\tan }^{-1}\left(\frac{3\mathrm{x}-{\mathrm{x}}^3}{1-3{\mathrm{x}}^2}\right)-{\tan }^{-1}\left(\frac{2\mathrm{x}}{1-{\mathrm{x}}^2}\right)$:

1. $0$

2. $1$

3. ${\tan }^{-1}\mathrm{x}$

4. ${\tan }^{-1}2\mathrm{x}$

Q. Find the maximum value of sin¹⁰⁰⁰x + cos²⁰⁰⁸x

Q.

Limit tends to π/2

Arc Cos[Cot X]

Where [ .] Represents greatest integer X

Q.

The value of Expression $(cos\frac{\pi }{2}+isin\frac{\pi }{2})$

$(cos\frac{\pi }{2^2}+isin\frac{\pi }{2^2})$...........to $\infty$is

1. -1

2. 1

3. 0

4. 2

Q.

The value of $tan[co{s}^{-1}\left(\frac{-2}{7}\right)-\frac{\pi }{2}]$ is

1. None

2. $\frac{2}{3\sqrt{5}}$
   

3. $\frac{3\sqrt{5}}{2}$
   

4. $\frac{2}{\sqrt{5}}$
   

Q.

If $\tan \left(\frac{\mathrm{\pi }}{4}+\mathrm{x}\right)+\tan \left(\frac{\mathrm{\pi }}{4}-\mathrm{x}\right)=\mathrm{a}$ then find the value of ${\tan }^2\left(\frac{\mathrm{\pi }}{4}+x\right)+{\tan }^2\left(\frac{\mathrm{\pi }}{4}-x\right)$.

Q. For any acute angle $\theta ,\sin (\pi +\theta )=$, $\cos (\pi +\theta )=$.

1. $-\sin \theta$
2. $-\cos \theta$
3. $\cos \theta$
4. $\sin \theta$

Q. The range of the function f(x)= sin^-1 square root(mod of x – x² is

Q. If $co{t}^{-1}\left(0.2\right)=c,then{\tan }^{-1}(-5)=$

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

Q.

The value of $tan[co{s}^{-1}\left(\frac{-2}{7}\right)-\frac{\pi }{2}]$ is

1. $\frac{2}{3\sqrt{5}}$

2. $\frac{3\sqrt{5}}{2}$

3. $\frac{2}{\sqrt{5}}$

4. None

Q. The number of solutions for the equation ${\cos }^{-1}\left(\cos x\right)=-\frac{1}{2}$ is

1. 1
2. infinite
3. \N
4. 2

Q. I, sir!!-2

Q.

$co{s}^{-1}\left(cos\frac{7\pi }{6}\right)=$

1. None of these

2. 
3. 
4. 

Q. What is the value of $(1+\cos \frac{\pi }{8})(1+\cos \frac{3\pi }{8})(1+\cos \frac{5\pi }{8})(1+\cos \frac{7\pi }{8})$?

1. $\frac{1}{2}$
2. $\frac{1}{2}+\frac{1}{2\sqrt{2}}$
3. $\frac{1}{2}-\frac{1}{2\sqrt{2}}$
4. $\frac{1}{8}$

Q. Find the minimum value of the function
$f\left(x\right)=\frac{{\pi }^2}{16{\cot }^{-1}(-x)}-{\cot }^{-1}x.$

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

Q. 9, cos' (-

Q. Find the minimum value of the function
$f\left(x\right)=\frac{{\pi }^2}{16{\cot }^{-1}(-x)}-{\cot }^{-1}x.$

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

Q. $co{t}^{-1}\left(0.2\right)=c,thenfindta{n}^{-1}(-5).$

1. - c
2. 2c
3. None of these
4. $\frac{c}{2}$

Q. If $y={\tan }^{-1}\frac{3x-x^3}{1-3x^2}$ then find $\frac{dy}{dx}$.

Q.

Prove That ${\tan }^{-1}\left(\frac{1}{3}\right)+{\tan }^{-1}\left(\frac{1}{5}\right)+{\tan }^{-1}\left(\frac{1}{7}\right)+{\tan }^{-1}\left(\frac{1}{8}\right)=\frac{\mathrm{\pi }}{4}$

Q. $Ifta{n}^{-1}\left(a\right)=\frac{\pi }{4}thenfindta{n}^{-1}(-a).$

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

Q. $Ifco{s}^{-1}\left(a\right)=\theta whereaϵ[-1,1]thenfindco{s}^{-1}(-a).$

1. Doesn't exist
2. $-\theta$
3. None of these
4. $\theta$

Q. The value of $cos\left(\frac{1}{2}co{s}^{-1}\left[cos\right(-14\frac{\pi }{5}\left)\right]\right)$

1. $cos\left(\frac{9\pi }{5}\right)$
2. $sin\left(\frac{-\pi }{5}\right)$
3. $cos\left(\frac{2\pi }{5}\right)$
4. $-cos\left(\frac{3\pi }{5}\right)$

Q.

$co{s}^{-1}x\{-cos\left(\frac{-13\pi }{6}\right)\}$ is equal to

1. $-\frac{\pi }{6}$
   

2. None

3. $\frac{5\pi }{6}$
   

4. $\frac{\pi }{6}$
   

Q. If $x$ is positive, the values of $f\left(x\right)=-3\cos \sqrt{3+x+x^2}$ lies in the interval

1. $[-1,3]$
2. $[-3,3]$
3. $[0,3]$
4. $[-3,0]$

Q. $co{t}^{-1}\left(0.2\right)=c,thenfindta{n}^{-1}(-5).$

1. - c
2. 2c
3. $\frac{c}{2}$
4. None of these

Q. $Ifco{s}^{-1}\left(a\right)=\theta whereaϵ[-1,1]thenfindco{s}^{-1}(-a).$

1. $\theta$
2. $-\theta$
3. Doesn't exist
4. None of these