JEE Main & Advanced Mathematics Trigonometric Equations Half Angle Formulae

Half Angle Formulae

Category : JEE Main & Advanced

If 2s shows the perimeter of a triangle ABC then, i.e., $2s=a+b+c,$ then

(1) Formulae for $sin\frac{A}{2},sin\frac{B}{2},sin\frac{C}{2}$

(i) $\sin \frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{bc}}$

(ii) $\sin \frac{B}{2}=\sqrt{\frac{(s-a)(s-c)}{ca}}$

(iii) $\sin \frac{C}{2}=\sqrt{\frac{(s-a)(s-b)}{ab}}$

(2) Formulae for $cos\frac{A}{2},cos\frac{B}{2},cos\frac{C}{2}$

(i) $\cos \frac{A}{2}=\sqrt{\frac{s(s-a)}{bc}}$

(ii)  $\cos \frac{B}{2}=\sqrt{\frac{s(s-b)}{ca}}$

(iii) $\cos \frac{C}{2}=\sqrt{\frac{s(s-c)}{ab}}$

(3) Formulae for $tan\frac{A}{2},tan\frac{B}{2},tan\frac{C}{2}$

(i) $\tan \frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{s(s-a)}}$

(ii)  $\tan \frac{B}{2}=\sqrt{\frac{(s-c)(s-a)}{s(s-b)}}$

(iii) $\tan \frac{C}{2}=\sqrt{\frac{(s-a)(s-b)}{s(s-c)}}$

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