Trigonometric Ratio(sec,cosec,cot)

Q.

Given $\tan A=\frac{4}{3}$, find all other trigonometric ratios of A.

Q. Question 3
If sin A = $\frac{3}{4}$, calculate cos A and tan A.

Q. If $sin(x-y)=\frac{1}{2}$ , $sin(x+y)=\frac{\surd 3}{2}$, and$0<y<x<{90}^{\circ }$, find the value of x and y, respectively.

1. 45°, 15°
2. 30°, 45°
3. 30°, 45°
4. 45°, 60°

Q.

Express $\tan 68°+\sec 68°$ in terms of trigonometric ratio of angles lying between $0°$ and ${45}^{\circ }$

Q. Given 15 cot A = 8, find sin A.

1. $\frac{15}{17}$
   
2. $\frac{8}{17}$
   
3. $\frac{17}{15}$
   
4. $\frac{15}{8}$
   

Q.

What is the value of tan θ in the given triangle?

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

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

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

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

Q. Find the value of $\frac{tan{63}^{\circ }+cot{23}^{\circ }}{tan{27}^{\circ }+cot{67}^{\circ }}-tan{63}^{\circ }tan{67}^{\circ }$

Q.

The value of $(\tan 1°\tan 2°\tan 3°\cdots \cdots \cdots \cdots \cdots \cdots \tan 89°)$ is

1. $0$

2. $1$

3. $2$

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

Q. In $△ABC,$ sin C = $\frac{3}{5}.$ Match the given trigonometric ratios with their values.

1. $\frac{4}{5}$
2. $\frac{3}{4}$
3. $\frac{5}{3}$
4. $\frac{5}{4}$

Q. If cotA = $\frac{4}{3}$, then $\frac{(1-ta{n}^{2}A)}{(1+ta{n}^{2}A)}=co{s}^{2}A-si{n}^{2}A$.

1. False
2. True

Q. Solve $\sin x+\sin y=\sin (x+y)$ and $|x|+|y|=1$.

Q. Match the terms having same value.

1. $tan{47}^{\circ }$
2. $cot{73}^{\circ }$
3. $sin{52}^{\circ }$
4. $cos{26}^{\circ }$

Q.

At $\theta ={90}^{\circ }$, which of the two angles are not defined?

1. $tan\theta ,cosec\theta$

2. $cot\theta ,sin\theta$

3. $cot\theta ,tan\theta$

4. $tan\theta ,sec\theta$

Q.

If $pcot\theta =\sqrt{q^2-p^2}$, then the value of $sin\theta$ is___.

1. $\frac{p}{q}$

2. $\frac{q}{2p}$

3. $\frac{q}{3p}$

4. 0

Q. $Statetrueorfalse$
$tan{1}^{\circ }.tan{89}^{\circ }=tan{2}^{\circ }.tan{88}^{\circ }$

1. True
2. False

Q. Which of the following statements hold true for a quadrilateral ABCD?

1. $sin\left(\frac{A+B}{4}\right)=cot\left(\frac{C+D}{4}\right)$
2. $sin\left(\frac{A+B}{4}\right)=cos\left(\frac{C+D}{4}\right)$
3. $tan\left(\frac{A+C}{4}\right)=cot\left(\frac{B+D}{4}\right)$
4. $tan\left(\frac{A+C}{4}\right)=cos\left(\frac{B+D}{4}\right)$

Q. Find the values of $cot\theta andcosec\theta$ in the figure given above.

1. $\frac{5}{2},2$
2. $\frac{4}{3},\frac{5}{3}$
3. $2,\frac{5}{4}$
4. $2,\frac{5}{2}$

Q. Which of the following statements is/are true for $\theta$ ranging from $0^{\circ }$ to ${90}^{\circ }$?

1. $cos\theta ,cot\theta andcosec\theta$ increases as $\theta$ increases.
2. $sin\theta =cos\theta$ for all the values of $\theta$
3. $sin\theta ,tan\theta andsec\theta$ increases as $\theta$ increases.
4. Trigonometric ratios values do not follow any pattern.

Q. For an acute angle $\theta ,$ $\text{tan}\theta \times \text{cot}\theta$ is 1.

1. False
2. True

Q. If $tan\theta$ = 2, then $cot\theta$ = $\frac{1}{2}$

1. False
2. True

Q. Evaluate: (${\text{cosec 31}}^{\circ }-\sec {59}^{\circ }$)(${\text{cosec 31}}^{\circ }+\sec {59}^{\circ }$)
[2 Marks]