Trigonometric Ratios of a Right Triangle

Q.

If $\sin \left(\theta \right)+\mathrm{cosec}\left(\theta \right)=2$, then the value of ${\sin }^{10}\left(\theta \right)+{\mathrm{cosec}}^{10}\left(\theta \right)$ is

1. $2$

2. $210$

3. $29$

4. $10$

Q.

Prove the following: $(\sqrt{3}+1)(3-\cot 30°)={\tan }^{3}60°-2\sin 60°$

Q.

If $5\tan \theta =4,$ then the value of $\frac{(5\sin \theta -4\cos \theta )}{(5\sin \theta +4\cos \theta )}$ is

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

2. $\frac{5}{6}$

3. $\frac{1}{6}$

4. 0

Q.

Is $cot$ inverse of $\tan ?$

Q.

In a $△ABC$, if $\left(\sqrt{3}-1\right)a=2b,A=3B,\mathrm{then}\angle C$ is equal to

1. $60°$

2. $120°$

3. $30°$

4. $45°$

Q. If $tanA=\frac{3}{4}$, then find the value of $\frac{SinA+CosA}{SinA-CosA}$.

1. -7

Q. $\sin \theta$ is equal to opposite side divided by hypotenuse.

1. True
2. False

Q.

AB is a chord of a circle with centre O. If $\angle AOB={50}^{\circ }$ and AB = 18 cm, the diameter of the circle will be equal to $sin{25}^{\circ }=0.42$

1. 46.25 cm

2. 40.25 cm

3. 42.85 cm

4. 44.50 cm

Q.

The diagonal of a rectangle is 20 cm and it makes an angle of ${40}^{\circ }$ with one of its sides.The perimeter of the rectangle will be equal to $[sin{40}^{\circ }=1.64,cos{40}^{\circ }=0.76]$

1. 56.24 cm

2. 65.25 cm

3. 48.5 cm

4. 58.5 cm

Q.

AB is a chord of a circle with centre O. If $\angle AOB={70}^{\circ }$ and AB=16 cm, the diameter of the circle will be $[sin{35}^{\circ }=0.57]$

1. 32.2 cm

2. 30.8 cm

3. 26.4 cm

4. 28.07 cm

Q.

If $\cos P=\frac{1}{7}$ and $\cos Q=\frac{13}{14}$ where $P$ and $Q$ both are acute angles.

Then the value of $P-Q$ is

1. $30°$

2. $60°$

3. $45°$

4. $75°$

Q. Which of the following trigonometric ratios have same values?

1. $sin{0}^0,cos{0}^0$
2. $sin{30}^0,cos{60}^0$
3. $tan{30}^0,cosec{60}^0$
4. $cos{90}^0,cosec{90}^0$

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

Find $sin(A+B-C)$

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

Q.

If 15 cot A = 8, find sin A and sec A. $\left[2\text{Marks}\right]$

Q. Prove that $2se{c}^2\theta -se{c}^4\theta -2cose{c}^2\theta +cose{c}^4\theta -ta{n}^4\theta$ [3 MARKS]

Q. In any right-angled triangle, for an acute angle $\theta ,$
$\text{sin}\theta$ = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}.$

1. False
2. True

Q. Which of the following ratio relates to opposite side of an angle and the hypotenuse in a right-angled triangle?

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

Q.

Find the value of $1+\cos \theta$

Q.

Using trigonometric tables, find the value of $(sin{64}^{\circ }{42}^{\prime }+cos{42}^{\circ }{20}^{\prime })$

1. 1.234

2. 1.6433

3. 1.986

4. 1.5623

Q. $\Delta ABC$ is right angled at C. Find cos B.

1. $\frac{AC}{BC}$
2. $\frac{AC}{AB}$
3. $\frac{BC}{AB}$
4. $\frac{AB}{BC}$

Q. The value of $9se{c}^{2}A-9{\tan }^{2}A$ is:

1. -1
2. 9
3. -9
4. 1

Q. Given $15\cot A=8$, find $\sin A$ and $\sec A$.

Q. If $\tan 2A=\cot (A-{18}^{\circ })$, where $2A$ is an acute angle, find the value of $A$.

Q. In any right-angled triangle, for an acute angle $\theta ,$
$\text{sin}\theta$ = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}.$

1. False
2. True

Q. $\Delta ABC$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find tan B.

1. $\frac{3}{4}$
2. $\frac{8}{6}$
3. $\frac{6}{10}$
4. $\frac{8}{10}$

Q.

Using trigonometric tables, find the value of $\frac{sin{64}^{\circ }{42}^{\prime }+cos{42}^{\circ }{20}^{\prime }}{tan{36}^{\circ }{40}^{\prime }+cot{63}^{\circ }{20}^{\prime }}$

1. 1.80

2. 1.31

3. 1.013

4. 1.89

Q. If $tan\theta =\frac{5}{12}$, find $\frac{(1+cos\theta )\times (1-sin\theta )}{(1+sin\theta )\times (1-cos\theta )}$.

Q.

Q. Find the value of
$sin\theta +cos\theta \text{, when}\theta ={45}^{\circ }$

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

Q. $2ta{n}^2{45}^{\circ }+3co{s}^2{30}^{\circ }-si{n}^2{60}^{\circ }$ = ________ .