Domain and Range of Trigonometric Ratios

Q. If $\theta$ is an acute angle and $sin\theta =\frac{p-6}{8-p},$ then p must satisfy

1. < 8
2. < 7
3. 
4. < 7

Q. If $cose{c}^2\theta =\frac{4xy}{(x+y{)}^2}$, then

1. 
2. 
3. 
4. 

Q.

The value of $sin\theta +cos\theta$ will be greatest when

1. 

2. 

3. 

4. 

Q.

If $|cos\theta +\{sin\theta +\sqrt{si{n}^2\theta +si{n}^2\alpha }\}|\le k$, then the value of k is

1. 

2. 

3. 

4. 

Q. The maximum value of $cos{\alpha }_1.cos{\alpha }_2......cos{\alpha }_n,$
under the restrictions $0\le {\alpha }_1{\alpha }_2,.....,{\alpha }_n\le \frac{\pi }{2}andcot{\alpha }_1.cot{\alpha }_2......cot{\alpha }_n=1$ is

1. 
2. 
3. 
4. 

Q. If $sinx+cosecx=2,thensi{n}^{n}x+cose{c}^{n}x$ is equal to

1. 
2. 
3. 
4. 

Q.

$Iff\left(x\right)=co{s}^{2}x+se{c}^{2}x,then$

1. f(x) 2

2. f(x) <1

3. f(x) = 1

4. 1 < f(x) < 2

Q.

For 0< $\varphi$ < $\frac{\pi }{2},ifx={\sum }_{n=0}^{\infty }co{s}^{2n}\varphi ,y={\sum }_{n=0}^{\infty }si{n}^{2n}\varphi ,z={\sum }_{n=0}^{\infty }co{s}^{2n}\varphi ,then$

1. xyz = xz + y

2. xyz = xy + z

3. xyz = x + y + z

4. xyz = yz + x

Q. If $A=si{n}^8\theta +co{s}^{14}\theta ,$ then for all real values of $\theta$

1. 
2. 1 <
3. 
4. 0 <

Q.

If 2 cos x +sin x =1 then 7 cos x +6 sin x=___

1. 6

2. 2

3. 1

4. 3