Trigonometric Ratios of Complementary Angles

Q. Evaluate $\left(\frac{\tan {45}^{\circ }}{cosec{30}^{\circ }}\right)+\left(\frac{\sec {60}^{\circ }}{\cot {45}^{\circ }}\right)-\left(\frac{5\sin {90}^{\circ }}{2\cot 0^{\circ }}\right)$

Q. Find the value of: $\frac{\cos {70}^{\circ }}{\sin {20}^{\circ }}+\frac{\cos {59}^{\circ }}{\sin {31}^{\circ }}+\frac{\cos \theta }{\sin (90-\theta )}-8{\cos }^2{60}^{\circ }$

1. 5
2. 1
3. 9
4. 14

Q. Find the value of the following

$\left(i\right)\sin {60}^{\circ }\cos {30}^{\circ }+\cos {60}^{\circ }\sin {30}^{\circ }$

$\left(ii\right)\cos {30}^{\circ }\cos {60}^{\circ }–\sin {30}^{\circ }\sin {60}^{\circ }$

Q.

In $△\text{ABC}$, AB=8 cm, $\angle A={45}^{\circ }$, $\angle B={60}^{\circ }$.
Find the area of the triangle.

1. $24-16\sqrt{3}c{m}^2$

2. $48-16\sqrt{3}c{m}^2$

3. $48-8\sqrt{3}c{m}^2$

4. $48-32\sqrt{3}c{m}^2$

Q. Find the value of cos19°59'.
(Refer the trigonometric table for the values)

1. 0.9398
2. 0.9938
3. 0.9598
4. 0.9893

Q. Evaluate $\left(\frac{\tan {45}^{\circ }}{cosec{30}^{\circ }}\right)+\left(\frac{\sec {60}^{\circ }}{\cot {45}^{\circ }}\right)-\left(\frac{5\sin {90}^{\circ }}{2\cot 0^{\circ }}\right)$

Q. Find the value of sin20°15'.
(Refer the trigonometric table for the values)

1. 0.5612
2. 0.6561
3. 0.3461
4. 0.5111

Q. Find the value of ${\cos }^2{60}^{\circ }+{\sec }^2{30}^{\circ }+{\tan }^2{45}^{\circ }$ ?

1. $\frac{12}{31}$
2. $\frac{31}{12}$
3. $0$
4. $\frac{11}{\sqrt{3}}$

Q. Find the value of the following:
$(\cos 0^{\circ }+\sin {45}^{\circ }+\sin {30}^{\circ })(\sin {90}^{\circ }-\cos {45}^{\circ }+\cos {60}^{\circ })$

Q. $cot{12}^{\circ }cot{38}^{\circ }cot{52}^{\circ }cot{60}^{\circ }cot{78}^{\circ }=$

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

Q. If $4{\sin }^2\theta -1=0$ and angle θ is less than ${90}^{\circ }$, find the value of θ and hence the value of ${\cos }^2\theta +{\tan }^2\theta$.

1. $\frac{13}{12}$
2. $\frac{12}{13}$
3. $\frac{7}{16}$
4. $\frac{16}{7}$

Q. If θ = ${30}^{\circ }$, prove that cos 2θ = cos² θ - sin² θ

Q. Find the value of $\sin {330}^{\circ }\cos {120}^{\circ }+\cos {210}^{\circ }\sin {300}^{\circ }$

Q. In $△ABC$,
$sin\left(\frac{A+B}{2}\right)=$

1. $cos\left(\frac{C}{2}\right)$
2. $-cos\left(\frac{C}{2}\right)$
3. $cos\left(\frac{C}{4}\right)$
4. $-cos\left(\frac{C}{4}\right)$

Q. If the value of $\sec \theta$ is 1, what is the value of $ta{n}^2\theta$?

1. 1
2. 1+$se{c}^2\theta$
3. 0
4. ${\tan }^2\theta +{\sec }^2\theta$

Q. Find the value of sec18°8'.
(Refer the trigonometric table for the values)

1. 0.9505
2. 1.0523
3. 1.1123
4. 1.0015

Q. Find the value of cosec15°7'.
(Refer the trigonometric table for the values)

1. 0.4512
2. 0.8744
3. 2.1134
4. 3.8343

Q. The value of cos39°44' - cos25°38' is .

1. $-$0.2225
2. $-$0.1545
3. $-$0.1131

Q. Find the value of cos25°28'.
(Refer the trigonometric table for the values)

1. 0.9235
2. 0.9028
3. 0.9512
4. 0.9817

Q. What is the tenths digit in the value of cos35°45'?

1. 8

Q. Find the value of 8sin 2x cos 4x sin 6x, when x = ${15}^{\circ }$

Q.

$\text{In}△$ ABC, $sin\left(\frac{A+B}{2}\right)=cos\left(\frac{C}{2}\right)$.

1. True

2. False

Q. Find the value of 8sin 2x cos 4x sin 6x, when x = ${15}^{\circ }$

Q. The value of $\sin 30.\cos 60+\cos 30.\sin 60$ is

Q. ${\left(\frac{\cos A+\cos B}{\sin A-\sin B}\right)}^n+{\left(\frac{\sin A+\sin B}{\cos A-\cos B}\right)}^n=x{\cot }^n\frac{A-B}{2}$ or a, accordingly as n is even or odd. Find $x+a$

Q. When we find cos 35°14', we subtract mean difference for 2' from the value of cos 35°12'.

1. True
2. False

Q. If θ = ${30}^{\circ }$, prove that cos 2θ = cos² θ - sin² θ

Q. $tan{48}^{\circ }tan{23}^{\circ }tan{42}^{\circ }tan{67}^{\circ }=$

1. 2
2. 0.5
3. 1
4. 0

Q. Find the value of the following:
$(\cos 0^{\circ }+\sin {45}^{\circ }+\sin {30}^{\circ })(\sin {90}^{\circ }-\cos {45}^{\circ }+\cos {60}^{\circ })$

Q. The value of cos69°45' - cos15°40' is .

1. $-$ 0.6168
2. 0.6168
3. $-$ 0.6618
4. 0.6618