In a triangle cos(A+B/2)=…

Correct Answer is : sinc2sinc/2sin2c

Correct Answer is : sinc2sinc/2sin2c

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AP DSC School Assistant Math Model Test 1

Section: Subject Specific

Question : 58 of 160

Marks: +1, -0

In a triangle

cos(\frac{A+B}{2})=…

Solution:

Concept:

In any triangle, the sum of the three angles is

180^\circ

, which gives a complementary angle relationship between half the sum of two angles and half the third angle.

Explanation:

1. In triangle

ABC

, we have

A + B + C = 180^\circ

2. Rearranging:

A + B = 180^\circ - C

3. Divide both sides by 2:

\frac{A+B}{2} = \frac{180^\circ - C}{2} = 90^\circ - \frac{C}{2}

4. Use the complementary angle identity:

\cos(90^\circ - \theta) = \sin \theta

5. Therefore,

\cos\left(\frac{A+B}{2}\right) = \cos\left(90^\circ - \frac{C}{2}\right) = \sin\left(\frac{C}{2}\right)

Answer:

Option D:

\sin\frac{c}{2}

(where

c

is angle

C

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