Standard Values of Trigonometric Ratios

Q. Find the acute angle $\left(\theta \right)$ at which
$sin\theta andtan\theta \text{are equal?}$

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. $0^{\circ }$
4. ${90}^{\circ }$

Q. Given:
$sin(B+C)=\frac{\sqrt{3}}{2}$
$sin(A+C)=sinB\text{and}$
$sinA=\frac{1}{2}.$

$\text{Find the value of}sin(A+B-C)?$

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

Q. At $\theta ={90}^{\circ }$ which of the following trigonometric ratios are not defined?

1. $tan\theta ,cosec\theta$
2. $cot\theta ,sin\theta$
3. $cot\theta ,tan\theta$
4. $tan\theta ,sec\theta$

Q. $Findthevalueofsi{n}^2\theta +co{s}^2\theta at\theta ={30}^{\circ }\&{60}^{\circ }$.

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

Q.

The value of expression $tan\theta -cot\theta at\theta ={30}^{\circ }$ is 1.

1. True
2. False

Q. Choose the correct option:
$\frac{2tan30^0}{1+ta{n}^2{30}^0}=$

[1 Mark]

(a) $sin{60}^{\circ }$
(b) $cos{60}^{\circ }$
(c) $tan{60}^{\circ }$
(d) $sin{30}^{\circ }$

Q.

$Ifsin(B+C)=\frac{\sqrt{3}}{2}andsinA=\frac{1}{2}$, find $B+CandA$.

1. $B+C={60}^{\circ }andA={30}^{\circ }$

2. $B+C={30}^{\circ }andA={30}^{\circ }$

3. $B+C={45}^{\circ }andA={60}^{\circ }$

4. $B+C={60}^{\circ }andA={60}^{\circ }$

Q. If $\theta$ is any acute angle, what is the area of a square with adjacent sides $sin\theta$ and $cosec\theta$?

1. 0
2. $sin\theta \times cos\theta$
3. $co{s}^2\theta$
4. $si{n}^2\theta$

Q.

If tan(A+B) =$\sqrt{3}$ and sin(A-B) = $\frac{1}{2}$ Where A and B are acute angles.

Then, Cos2A + Sin2B =__

Q.

If A=${45}^{\circ }$

Then, secA cotA –cosecA tanA =__