Trigonometric Ratios of Half Angles

Q.

If $A$ lies in the second quadrant and $3\tan A+4=0$ then the value of $2cotA-5\cos A+\sin A$ is equal to

1. $\frac{-53}{10}$

2. $\frac{-7}{10}$

3. $\frac{7}{10}$

4. $\frac{23}{10}$

Q. 62.C1/C0 +2C2/C1+3C3/C2+, , , , , , , =

Q. 73.Prove that in a triangle ABC, cosecA (sinBcosC +cosBsinC) is equals to 1.

Q. In $△$ ABC, if a = 16, b = 24 and c = 20, then cos $\frac{B}{2}$ =
[MP PET 1988]

1. 3/4
2. 1/4
3. 1/2
4. 1/3

Q.

Law of cosine is applicable if we know

1. (a) and (b) both

2. All three angles

3. Two sides and angle included

4. All three sides of a triangle

Q. In a triangle ABC if 3R equal to 4r then the value of 4(cosA + cosB+ cosç)is equal to

Q.

In the given figure below, as per law of cosine which is the correct formula

1. a²=b²+c²-2bc.cos B

2. a²=b²+c²+2bc.cos A

3. a²=b²+c²-2bc.cos A

4. a²=b²-c²-2bc.cos A

Q. If $\cos \frac{A}{2}=\sqrt{\frac{b+c}{2c}}$, then :

1. $a^2+b^2=c^2$
2. $c^2+b^2=a^2$
3. $a^2+c^2=b^2$

Q.

Law of cosine is applicable if we know

1. a) All three sides of a triangle

2. b) Two sides and angle included

3. c) All three angles

4. d) (a) and (b) both

Q.

In a triangle ABC, a = 3, b = 5, c = 7. Find the angle opposite to C.

1. ${60}^{\circ }$

2. ${90}^{\circ }$

3. ${120}^{\circ }$

4. ${150}^{\circ }$

Q. 10. If acose + bsine = 3 and asine - bcos0 = 4, then a^2 b^2 has the value