Trigonometric Ratios of Half Angles

Q.

How do you find the exact values of $\cos 22.5°$ using the half-angle formula?

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. In $△ABC,(a-b{)}^{2}co{s}^2\frac{C}{2}+(a+b{)}^{2}si{n}^2\frac{C}{2}=$

1. $a^2$
2. $b^2$
3. $c^2$
4. None of these

Q. In $△$ ABC, if cos A + cos C = 4 $si{n}^2\frac{1}{2}B,$ then a, b, c are in

1. A. P.

2. G. P.

3. None of these
4. H. P.

Q. If in a $\Delta$ ABC, perimeter is 12 units, b = 3 units, c = 5 units then find $sin\left(\frac{A}{2}\right)$.

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

Q. In $△$ ABC, if cos A + cos C = 4 $si{n}^2\frac{1}{2}B,$ then a, b, c are in

1. A. P.

2. G. P.

3. H. P.
4. None of these

Q.

In $△ABC,1-tan\frac{A}{2}tan\frac{B}{2}=$
[Roorkee 1973]

1. $\frac{2c}{a+b+c}$

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

3. $\frac{2}{a+b+c}$

4. $\frac{4a}{a+b+c}$

Q. In $△ABC,(cot\frac{A}{2}+cot\frac{B}{2})(asi{n}^2\frac{B}{2}+bsi{n}^2\frac{A}{2})=$
[Roorkee 1988]

1. cot C
2. c cot C
3. cot $\frac{C}{2}$
4. c cot $\frac{C}{2}$

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