Range of Trigonometric Expressions

Q. Find the derivative of the following function:
f(x) = $\frac{sinx+cosx}{sinx-cosx}$

Q.

The maximum value of $1+2\sin x+3{\cos }^{2}x$ is

1. $\frac{3}{13}$

2. $\frac{13}{3}$

3. $\frac{2}{13}$

4. $\frac{13}{2}$

Q.

Which of the values cannot be the value of sin θ?

1. 1/2

2. 1/√3

3. √3

4. √3/2

Q.

Minimum value of $5si{n}^2\theta +4co{s}^2\theta$ is

1. 1

2. 2

3. 3

4. 4

Q. If A sin (0 +a) = 4 cos 0 +4 sin 0, then the value ofα s

Q.

In any $\Delta ABC,$ prove that

$a^{3}sin(B-C)+b^{3}sin(C-A)+c^{3}sin(A-B)=0.$

Q. The possible value of sin–1(x2 + 4x + 5) is

Q. The range of $f\left(x\right)=\cos \left(\sqrt{x}\right)$ is

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

Q.

Evaluate: $\tan \frac{\mathrm{\pi }}{4}$

Q. Minimum value of the expression $4\sin (x-\frac{\pi }{6})-6\sqrt{2}\cos (x+\frac{\pi }{4})$ is

1. $-\sqrt{112+24\sqrt{3}}$
2. $-\sqrt{28+24\sqrt{3}}$
3. $-\sqrt{56+2\sqrt{3}}$
4. $-\sqrt{84+2\sqrt{3}}$

Q.

Value of sin35⁰cos45⁰

1. 

2. 

3. 

4. 

Q. $\mathrm{The}\mathrm{minimum}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{function}f\left(x\right)={\cos }^{2}x+{\sin }^{4}x\mathrm{is}$.

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

Q.

Find the maximum value of 5 + $(sinx-4{)}^2$

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Q. if x€(-infinity , -1)then find the value of 4 tan^-1x+sin^-1(2x/1+x^2)+cos^-1(1-x^2/1+x^2)

Q. Convert the given complex number in polar form : $-1+i$

Q. If ${\sin }^2\theta -2\sin \theta -1=0$ is to be satisfied for exactly 4 distinct values of $\theta \in [0,n\pi ],n\in N,$ then the least value of n is

1. 2
2. 6
3. 4
4. 15

Q.

If x and y are the maximum and minimum values of sin $\theta$ + cos $\theta$, find the value of $x^2$ + $y^2$

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Q. How to solve? sin^-1(sin23)=?

Q.

The value of a cos $\theta$ + b sin $\theta$ lies between

1. 

2. 

3. a-b and a+b

4. a and b

Q. Maximum value of the expression $\sqrt{{\cos }^{2}x-10\cos x+25}+3$ is

1. $7$
2. $9$
3. $3$
4. $4$

Q.

Let n be a positive integer such that $sin\frac{\pi }{2^n}+cos\frac{\pi }{2^n}=\frac{\sqrt{n}}{2}$. Then

1. $6\le n\le 8$

2. 4 < $n\le 8$

3. $4\le$ n < 8

4. 4 < n < 8

Q.

Let n be a positive integer such that $sin\frac{\pi }{2^n}+cos\frac{\pi }{2^n}=\frac{\sqrt{n}}{2}$. Then

1. 

2. 4 <

3. 4 < n < 8

4. n < 8

Q.

$\alpha ,\beta ,\gamma$ are real numbers satisfying $\alpha +\beta +\gamma =\pi$.

The value of the given expression

$sin\alpha +sin\beta +sin\gamma$ is

1. Zero

2. Positive

3. -3

4. Negative

Q.

Prove $x=(2n\pi +\frac{\pi }{2})$ or $x=2n\pi$, where $n\in I$.

Q. Minimum value of the expression $(4{\sin }^2\theta +12{\text{cosec}}^2\theta -13)$ is equal to ​​​​​​

Q.

The maximum value of 3cos $\theta$ - 4 sin$\theta$ is

1. 3

2. 4

3. 5

4. None of these

Q.

Let $f\left(x\right)=cosx(sinx+\sqrt{si{n}^{2}x+si{n}^2\theta }),\theta$ is a given const, then max of f(x)is

1. $\sqrt{1+cs{c}^2\theta }$

2. $\sqrt{1+si{n}^2\theta }$

3. $|cos\theta |$

4. $|sin\theta |$

Q.

Let $f\left(x\right)=cosx(sinx+\sqrt{si{n}^{2}x+si{n}^2\theta }),\theta$ is a given const, then max of f(x)is

1. $\sqrt{1+cs{c}^2\theta }$

2. $|sin\theta |$

3. $\sqrt{1+si{n}^2\theta }$

4. $|cos\theta |$

Q.

Express $\frac{(cos\theta +isin\theta {)}^4}{(sin\theta +icos\theta {)}^5}$ in a+ib form where i=$\sqrt{-1}$

1. 

2. 

3. 

4. 

Q.

The minimum value of $3sin\theta +4cos\theta$ is

1. 5

2. 3

3. -5

4. 1