This question is from trigonometry topic- trigonometric ratios on complementary angles in which we have to prove that tan(C+A)/2 = cotB/2, if A, B and C are the angles of a ΔABC

RS Aggarwal, Class 10, Chapter 12, question no 9.

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Given function is : tan (C + A)/2 = cot B/2

Sum of all the angles of a triangle = 180 degree

So, A + B + C = 180°

Or A + C = 180° – B

And, (A + C)/2 = (180° – B)/2 = 90° – B/2

Now, tan (A + C)/2

= tan(90° – B/2) = cot B/2

Hence Proved.