#### Question

If A, B, C are the interior angles of a triangle ABC, prove that

`tan ((C+A)/2) = cot B/2`

#### Solution

We have to prove: `tan((C + A)/2) = cot B/2`

Since we know that in triangle ABC

A + B + C = 180

`=> C + A = 180^@ - B`

`=> (C + A)/2 = 90^@ - B/2`

`=> tan (C + A)/2 = tan (90^@ - B/2)`

`=> tan (C + A)/2 = cot B/2`

Proved

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#### APPEARS IN

Solution If A, B, C Are the Interior Angles of a Triangle Abc, Prove that `Tan ((C+A)/2) = Cot B/2` Concept: Trigonometric Ratios of Some Specific Angles.