If sin -sin -a and cos-cos-bthen show that- sin - - - - 2ab-a2 - b2-

[ sin #160; ( α +β #160; ) = 2ab / a^ 2 + b^ 2 ...

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Solving Simultaneous Trigonometric Equations

If sin α+si...

Question

If $s i n α + s i n β = a$ and $c o s α + c o s β = b$
then show that, $sin (α + β) = \frac{2 a b}{a^{2} + b^{2}}$ .

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

sin α + sin β = a

cos α + cos β = b

sin α + β = \frac{m a b}{a^{2} + b^{2}}

m

sin α + sin β = a

cos α + cos β = b

tan \frac{α - β}{2} = \pm \sqrt{\frac{x - a^{2} - b^{2}}{a^{2} + b^{2}}}

x

If sin α + sin β = a

cos α + cos β = b

sin (α + β)

\frac{cos α}{cos β} = a

\frac{sin α}{sin β} = b

(a^{2} - b^{2}) {sin}^{2} β = a^{2} - 1

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