Does-sin-A-sin-B-imply-sin-A-2-sin-B-2-For-example-A-pi-and-B-pi-

Question Number 13305 by prakash jain last updated on 18/May/17

Does

\sin A = \sin B

imply \sin \frac{A}{2} = \sin \frac{B}{2} ?

For example A = π and B = - π ?

Answered by ajfour last updated on 18/May/17

A = n π + {(- 1)}^{n} B

w h e n \sin A = \sin B;

\sin \frac{A}{2} = \sin (\frac{n π}{2} + {(- 1)}^{n} \frac{B}{2})

f o r B = - π; A = π w e h a v e n = 2

\sin \frac{A}{2} = \sin (\frac{2 π}{2} + {(- 1)}^{2} \frac{B}{2})

\sin \frac{A}{2} = \sin (π + \frac{B}{2}) \neq \sin \frac{B}{2} .

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