If sin α+sin β=a and cos α+cos β=b, prove that (i) sin(α+β)=2ab – InterviewSolution

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If sin α+sin β=a and cos α+cos β=b, prove that (i) sin(α+β)=2aba2+b2 (ii) cos(α−β)=a2+b2−22

Answer»

If $s i n α + s i n β = a a n d c o s α + c o s β = b$ , prove that

(i) $s i n (α + β) = \frac{2 a b}{a^{2} + b^{2}}$

(ii) $c o s (α - β) = \frac{a^{2} + b^{2} - 2}{2}$

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