If A- B- C are the interior angles of a triangle ABC- prove thati tan C - A 2- B 2ii sin B - C 2-cos A 2

(i) We have to prove: Since we know that in triangle Proved nbsp; (ii) We have to prove: Since we know that in triangle Proved ...

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Range of Trigonometric Ratios from 0 to 90 Degrees

If A, B, C ar...

Question

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

(i) $\tan (\frac{C + A}{2}) = \cot \frac{B}{2}$
(ii) $\sin (\frac{B + C}{2}) = \cos \frac{A}{2}$

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Solution

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\sin (\frac{B + C}{2}) =

\sin \frac{A}{2}

\cos \frac{A}{2}

- \sin \frac{A}{2}

- \cos \frac{A}{2}

sin (\frac{B + C}{2}) =

t a n (\frac{C + A}{2}) = c o t \frac{B}{2}

\frac{sin (B - C)}{sin (B + C)} = \frac{b^{2} - c^{2}}{a^{2}}

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