If sin A-sin B- and cos A-cos B - then- write the value of tanA-B2 -

α #160;β = 2 sin(A+B2).cos(A B2)2cos(A+B2).cos(A B2) α #160;β = tan(A+B2) ...

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Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

If sin A+si...

Question

If $sin A + sin B = α$ and $cos A + cos B = β$ then, write the value of $tan (\frac{A + B}{2})$ ?

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Solution

$\frac{α}{β} = \frac{2 sin (\frac{A + B}{2}) . cos (\frac{A - B}{2})}{2 cos (\frac{A + B}{2}) . cos (\frac{A - B}{2})}$

$\frac{α}{β} = tan (\frac{A + B}{2})$

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