Question

If A + C = 2B, then `(cos C - cos A)/(sin A - sin C)` is equal to ______.

विकल्प

• cot B

• cot 2B

• tan 2B

• tan B

Answer 1

If A + C = 2B, then `(cos C - cos A)/(sin A - sin C)` is equal to tan B.

Explanation:

`(cos C - cos A)/(sin A - sin C)`

= `(2 sin ((A + C)/2) sin ((A - C)/2))/(2 cos ((A + C)/2) sin((A - C)/2)`

= `(2 sin B)/(2 cos B)`  ...[∵ A + C = 2B]

= tan B