Standard values

Q.

Given that sin A = $\frac{1}{2}$ and cos B = $\frac{1}{\sqrt{2}}$, then the value of (A + B) is ____.

$(Here,0<A+B\le {90}^{\circ })$

1. ${45}^{\circ }$

2. ${30}^{\circ }$

3. ${75}^{\circ }$

4. ${15}^{\circ }$

Q.

What is the value of $\tan \left(-1575°\right)$?

1. $1$

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

3. $0$

4. $-1$

Q.

In $△$ PQR, right angled at Q, PQ = 12 cm and PR = 12$\sqrt{2}$ cm. Determine $\angle$QPR and $\angle$ PRQ.

1. ${60}^{\circ }$ , ${30}^{\circ }$

2. ${30}^{\circ }$ , ${60}^{\circ }$

3. ${45}^{\circ }$ , ${45}^{\circ }$

4. ${22.5}^{\circ }$ , ${67.5}^{\circ }$

Q.

$△$ ABC, right angled at B, BC = 6 cm and ∠ABC = ${30}^{\circ }$. Determine the length of the side AB and AC.

1. 6$\sqrt{3}$ cm , 12cm

2. 4$\sqrt{3}$ cm , 12cm

3. 2$\sqrt{3}$ cm , 16cm

4. $\sqrt{3}$ cm , 16cm

Q.

If

$\Delta \left(x\right)=\left|\begin{array}{ccc}1& \cos x& 1-\cos x\\ 1+\sin x& \cos x& 1+\sin x-\cos x\\ \sin x& \sin x& 1\end{array}\right|$

then ${\int }_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\Delta \left(x\right)dx=$

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

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

3. $0$

4. $–\left(\frac{1}{4}\right)$

Q.

For the given statements select the correct option.

Assertion(A): The value of $sin{60}^{o}cos{30}^{o}sin{30}^{o}cos{90}^o$ is $0$.

Reason(R): $cos90°=0$.

1. (A) is false but (R) is true
2. Both (A) and (R) are true and (R) is not the correct explanation of (A).
3. Both (A) and (R) are true and (R) is the correct explanation of (A).
4. (A) is true but (R) is false

Q.

In $△PQR$ right angled at $Q$, $PR+QR=25cm$ and $PQ=5cm$ determine the values of $\sin \left(P\right)$.

Q.

Find the value of $\theta$, in the right triangle $△$ ABC.

__

Q.

In triangle ABC, right angled at B, if one angle is ${45}^{\circ }$, find the value of sin A and cos C.

1. 2, 2

2. $\frac{1}{\sqrt{2}}$, $\frac{1}{\sqrt{2}}$

3. $\frac{1}{\sqrt{3}}$, $\frac{1}{\sqrt{3}}$

4. 1, 1

Q. The value of $4co{t}^2{45}^{\circ }-se{c}^2{60}^{\circ }+si{n}^2{60}^{\circ }+co{s}^2{90}^{\circ }$ is

1. $\frac{1}{2}$
2. $0$
3. $\frac{5}{2}$
4. $\frac{3}{4}$

Q. $(\sec A+\tan A-1)(\sec A-\tan A+1)=$

1. $2\sin A$
2. $2\cos A$
3. $2\sec A$
4. $2\tan A$

Q.

For what value of A is sin A = cos A?

1. 0°

2. 30°

3. 90°

4. 45°

Q. In $△$ABC, $\angle B={90}^{\circ }$.

If $tanA=\frac{1}{\sqrt{3}}$, then

$sinA.cosC+cosA.sinC$ = ___

Q. The value of $cosec{30}^{\circ }+cot{45}^{\circ }$ is

1. 1
2. 2
3. 3
4. 4

Q.

The value of sin ${90}^{\circ }$ and cos $0^{\circ }$ are:

1. 0, 1

2. 1, 0

3. 0, 0

4. 1, 1

Q. What is the value of cot A if the value of sin A = 1/2?

1. 1
2. sq root(3)
3. 1/sq root(3)
4. sq root(3)/2

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

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

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

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