# If A, B and C Are the Angles of a δAbc, Prove that Tan ( C + a 2 ) = Cot B 2 - Mathematics

Sum

If A, B  and C are the angles of a  ΔABC, prove that tan ((C + "A")/2) = cot  B/2

#### Solution

In ΔABC

A + B + c = 180°

⇒ A + C = 180° - B      ..........(i)

Now,

LHS = tan (("C"+"A")/2)

=tan ((180^circ - "B")/2)           [Using (i)]

= tan (90^circ - "B"/2)

= cot  "B"/2

= RHS

Concept: Trigonometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 7 Trigonometric Ratios of Complementary Angles
Exercises | Q 9 | Page 314

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