Range of Trigonometric Ratios from 0 to 90 Degrees

Q.

Evaluate: $\frac{\sin {30}^{\circ }+\tan {45}^{\circ }-\text{cosec}{60}^{\circ }}{\sec {30}^{\circ }+\cos {60}^{\circ }+\cot {45}^{\circ }}$

Q.

If $\tan A=\frac{a}{(a+1)}$ and $\tan B=\frac{1}{(2a+1)}$, then the value of $A+B$ is?

Q.

Evaluate the following: $2{\tan }^{2}45°·{\cos }^{2}30°·{\sin }^{2}60°$.

Q.

Evaluate $\left(\frac{\sin 70°+\cos 40°}{\cos 70°+\sin 40°}\right)$:

1. $1$

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

3. $\sqrt{3}$

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

Q. If $tan\theta =1$, then find the value of $\theta$.

1. $0^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. Question 9
If $\sqrt{3}tan\theta =1$, find the value of $si{n}^2\theta -co{s}^2\theta$.

Q.

The value of tan A is always less than 1, for any value of A between $0^{\circ }$ and ${90}^{\circ }$.

1. True

2. False

Q. Question 10
If $sin\alpha =\frac{1}{2}$ and $cos\beta =\frac{1}{2}$, then the value of $(\alpha +\beta )$ is

(A) $0^{\circ }$
(B) ${30}^{\circ }$
(C) ${60}^{\circ }$
(D) ${90}^{\circ }$

Q.

If 1+ sin² A = 3sinAcosA , then prove that tanA=1 or 1/2

Q.

$\sec A=(\frac{12}{5}$) for some value of angle $A$. Is it True/False?

1. False

2. True

Q. If in a triangle $ABC,a=5,b=4$ and $\cos (A-B)=\frac{31}{32}$. then the third side $c$ is equal to

1. 3
2. 6
3. 7
4. 9

Q. Write the maximum and minimum values of sin θ.

Q.

The value of $\cos \left(105°\right)+\sin \left(105°\right)$ is

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

2. $1$

3. $\sqrt{2}$

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

Q.

$sinA=\frac{4}{3}$ for some angle A. State True/False.

1. True

2. False

Q.

How do you find the value of $cot0°$?

Q.

If tan theta = 12/5, then find the value of 1+sin theta/ 1- sin theta

Q.

What are the steps to solve trigonometric equations?

Q. 131.Prove that :- cos A / (1 - tan A) + sin A / (1- cot A) = sin A + cos A

Q. Question 9
The value of $2sin\theta$ can be $a+\frac{1}{a}$, where a is a positive number and $a\ne 1$.

Q. If SecA = x +1/4x, then prove that sec A+tan A=2x or 1/2x

Q. Question 15
A ladder against a vertical wall at an inclination $\alpha$ to the horizontal. Its foot is pulled away from the wall through a distance p, so that is upper end slides a distance q down the wall and then the ladder makes an angle $\beta$ to the horizontal. Show that $\frac{p}{q}=\frac{cos\beta -cos\alpha }{sin\alpha -sin\beta }$

Q.

The value of tan A is always less than 1.

1. True

2. False

Q.

prove (sin a ÷1+cos) +(1+cos a÷sin a)=2 cosec a

Q.

If $x=\sin 130°\cos 80°,y=\sin 80°\cos 130°,z=1+xy$ which one of the following is true?

1. $x>0,y>0,z>0$

2. $x>0,y<0,0<z<1$

3. $x>0,y<0,z>0$

4. $x<0,y<0,0<z<1$

Q.

tan²A-sin²A=tan²AsinA²

Q.

Evaluate $\tan {20}^{°}\tan {40}^{°}\tan {60}^{°}\tan {80}^{°}$

1. $1$

2. $2$

3. $3$

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

Q. If √3 tanA = 3 sinA
Then prove that:- sin²A – cos²A= 1/3

Q. If $tan\theta =1$, then find the value of $\theta$.

1. $0^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q.

$\sin A=\frac{4}{3}$ for some value of $A.$

1. False

2. True

Q. If (cos⁴A/cos²B) + (sin⁴A/sin²B) = 1
Prove that
(cos⁴B/cos²A) + (sin⁴B/sin²A) = 1