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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