Trigonometric Ratios of Complementary Angles

Q. $\frac{sin25°}{cos65°}+\frac{tan23°}{cot67°}$ =_______

1. 3
2. 0
3. 2
4. 1

Q.

sin (55° - A) - cos (35° + A) = ___.

1. 2

2. 1

3. 0

4. -1

Q.

$\frac{1+sin({90}^{\circ }-\theta )-{cos}^2({90}^{\circ }-\theta )}{cos({90}^{\circ }-\theta )[1+sin({90}^{\circ }-\theta \left)\right]}=$

1. $\text{cot}\theta$

2. $\text{tan}\theta$

3. 1

4. 0

Q.

If A, B, C are the angles of a triangle, then
$\sin \left(\frac{B+C}{2}\right)=$ ___.

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

2. $\tan \frac{A}{2}$

3. $\cot \frac{A}{2}$

4. $\cos \frac{A}{2}$

Q.

The value of $\frac{co{s}^2{26}^{\circ }+co{s}^2{64}^{\circ }}{si{n}^2{55}^{\circ }+si{n}^2{35}^{\circ }}$ is:

(find out, without using trignometric tables)

1. 1

2. -1

3. 0

4. not defined

Q. $sin{49}^{\circ }.tan{11}^{\circ }.sec{41}^{\circ }.tan{79}^{\circ }=$________.

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

Q.

Calculate $\frac{\text{sin}{70}^{\circ }}{\text{cos}{20}^{\circ }}+\frac{\text{cosec}{36}^{\circ }}{\text{sec}{54}^{\circ }}-2\text{cos}{43}^{\circ }\text{cosec}{47}^{\circ }$.

1. 2

2. 1

3. -1

4. 0

Q.

Find the value of the following expression.
$\frac{\tan {82}^{\circ }}{\cot 8^{\circ }}+\frac{cosec{38}^{\circ }}{\sec {52}^{\circ }}+\frac{2\sin {35}^{\circ }\sec {55}^{\circ }}{{\sin }^2{50}^{\circ }+{\sin }^{2}40}$

1. 4

2. 3

3. 2

4. 1

Q.

Express $(sin{75}^{\circ }+cosec{75}^{\circ })$ in terms of trigonometric ratios of angles between $0^{\circ }$ and ${15}^{\circ }.$

1. $(sec{15}^{\circ }+sin{15}^{\circ })$
2. $(cos{45}^{\circ }+sec{45}^{\circ })$
3. $(cos{15}^{\circ }+sec{15}^{\circ })$
4. $(cos{25}^{\circ }+sec{25}^{\circ })$

Q.

$\frac{\text{sec}{17}^{\circ }}{\text{cosec}{73}^{\circ }}+\frac{\text{tan}{68}^{\circ }}{\text{cot}{22}^{\circ }}-[{\text{cos}}^2{44}^{\circ }+{\text{cos}}^2{46}^{\circ }]=$___.

1. -1

2. 2

3. 1

4. 0