Complementary Ratios

Q.

If $\frac{\sin (x+y)}{\sin (x-y)}=\frac{\left(a+b\right)}{\left(a-b\right)}$then $\frac{\tan x}{\tan y}$ is equal to

1. $\frac{a^2}{b^2}$

2. $\frac{a}{b}$

3. $\frac{b}{a}$

4. $\frac{\left(a^2+b^2\right)}{\left(a^2-b^2\right)}$

Q.

Evaluate: $\tan \frac{\mathrm{\pi }}{2}$

Q.

If sec θ+tan θ=k then find the value of sec θ​ - tan θ in terms of k.

Q.

If sec5A = cosec(A-30), then the value of A is ___.

Q.

Evaluate :
$tan{26}^{\circ }/cot{64}^{\circ }$___

1. 1

2. 2

3. 0

4. -1

Q. If the value of $tan\alpha =\frac{5}{2}$, then find the value of $cot\theta$.
Given : $\alpha +\theta ={90}^{\circ }.$

1. $5$
2. $\frac{5}{\sqrt{21}}$
3. $\frac{5}{2}$
4. $\frac{\sqrt{21}}{2}$

Q.

The radian measure of $175°45$ is

Q. In $△ABC$,
$sec\left(\frac{B+C}{2}\right)=$ _______.

1. $-cosec\left(\frac{A}{2}\right)$
2. $-sec\left(\frac{A}{2}\right)$
3. $sec\left(\frac{A}{2}\right)$
4. $cosec\left(\frac{A}{2}\right)$

Q.

The tangent (tan) of an angle in a right-angled triangle is defined as

1. The ratio between the lengths of opposite side of the angle to its adjacent side.

2. The ratio between the lengths of opposite side of the angle to its hypotenuse.

3. The ratio of the length of an adjacent side of an angle to the length of its hypotenuse.

4. The ratio between the lengths of adjacent side of the angle to its hypotenuse.

Q.

If $sin\theta =cos\theta$, then value of $\theta$ is

1. 90 degrees

2. 0 degrees

3. 45 degrees

4. 30 degrees

Q.

Which of the following options is equal to the given expresssion?

$\frac{cot({90}^{\circ }-\theta )}{cose{c}^2\theta }\times \frac{sec\theta .co{t}^3\theta }{si{n}^2({90}^{\circ }-\theta )}$

1. $tan\theta$
2. $sec\theta$
3. $cos\theta$
4. $\sqrt{1+se{c}^2\theta }$

Q. Question 2 (iii)
Choose the correct option and justify your choice.
(iii) $sin2A$ = 2sinA is true when A =
(A) $0^{\circ }$
(B) ${30}^{\circ }$
(C) ${45}^{\circ }$
(D) ${60}^{\circ }$

Q. In $△ABC$,
$tan\left(\frac{B+C}{2}\right)=$ _______.

1. $cot\left(\frac{A}{2}\right)$
2. $-cot\left(\frac{A}{2}\right)$
3. $-tan\left(\frac{A}{2}\right)$
4. $-tan\left(\frac{A}{2}\right)$

Q.

In the given triangle right angled at B, which pair of angles are complementary?

1. B and C

2. A and B

3. C and A

4. None of the above

Q.

What is $tan\theta$ in $△ABC$, if $\theta$ is increased by ${30}^{\circ }$?

1. Not defined.

2. $\sqrt{3}$

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

4. $0$

Q. $sin2A=2sinA$ is true when A =

1. 60
2. 0
3. 30
4. 45

Q. Question 3
Write ‘True’ or ‘False’ and justify your answer in each of the following:​​​​​​​
The value of the expression,
$(sin{80}^{\circ }-cos{80}^{\circ })$ is negative.

Q.

If sin[90 - (A+B)] = cosx = cosy

find the value of x and y; if y is the angle C of triangle ABC. (In triangle ABC, A+B=${90}^{\circ }$)

1. x = A+B; y=C

2. x=A+B; y =${90}^{\circ }$

3. both (a) and (b)

4. none of these

Q. if $sin10A^{\circ }=cos(2A-30{)}^{\circ }$, then the value of A in degrees is ____ .

1. $A={10}^{\circ }$
2. $A={30}^{\circ }$
3. $A={40}^{\circ }$
4. $A={20}^{\circ }$

Q.

$sin(60+\theta )-cos(30-\theta )$ is equal to_____ if $(60+\theta )$ and $(30-\theta )$ are acute angles.

1. 1

2. 2 cos

3. 2 sin

4. 0

Q.

Which of the following options is equal to the given expresssion?

$\frac{cot({90}^{\circ }-\theta )}{cose{c}^2\theta }$ $\times$ $\frac{sec\theta .co{t}^3\theta }{si{n}^2({90}^{\circ }-\theta )}$

1. 

2. 

3. 

4. 

Q.

$\frac{sin(90-\theta )cos(90-\theta )}{cot(90-\theta )}$ + $si{n}^2\theta$ =

__

Q.

Say True or False:
In a triangle, if a pair of angles is complementary, then the triangle is a right-angled triangle.

1. True

2. False

Q. Question 3
The value of the expression $cosec({75}^{\circ }+\theta )-sec({15}^{\circ }-\theta )-tan({55}^{\circ }+\theta )+cot({35}^{\circ }-\theta )$ is

(A) -1
(B) 0
(C) 1
(D) $\frac{3}{2}$

Q.

How do you find the value of $\tan \left(\frac{\mathrm{\pi }}{3}\right)$?

Q. State true or false.
In $△ABC$, $sin\left(\frac{A+B}{2}\right)=cos\left(\frac{C}{2}\right)$

1. True
2. False

Q. If tan2A = cot(A-${18}^{\circ }$), then the value of angle A in degrees is _____.

1. 36

Q. $\frac{\cos ({90}^{\circ }+\theta )\sec (-\theta )\tan ({180}^{\circ }-\theta )}{\sin ({360}^{\circ }+\theta )\sec ({180}^{\circ }+\theta )\cot ({90}^{\circ }-\theta )}$ is equal to

1. $2$
2. $-1$
3. $1$
4. $0$

Q. If the value of tan α=52, then the value of cotθ if α+θ=90∘ equals .

1. $\frac{5}{\sqrt{21}}$
2. $5$
3. $\frac{5}{2}$
4. $\frac{\sqrt{21}}{2}$

Q.

If $tan2A=cot(A-{18}^{\circ })$, then value of $A$ is ((A - 18) & 2A are acute angle)

1. 

2. 

3. 

4.