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If A, B, C Are the Interior Angles of a Triangle Abc, Prove that `Tan ((C+A)/2) = Cot B/2` - CBSE Class 10 - Mathematics

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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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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.
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