Question

if
$\cos(a) + \cos(b) = \frac{1}{2}$
and
$\sin(a) + \sin(b) = \frac{1}{4}$
then find the value of
$\tan( \frac{a + b}{2} )$

Answer 1

★ TRIGONOMETRIC REDUCTIONS ★

Given that ,

Cos a + Cos b = 1/2

Sin a + Sin b = 1/4

Sin a + Sin b = 2 Sin ( a + b /2 ) Cos (a - b /2)

Cos a + Cos b = 2 Cos (a + b /2) Cos ( a - b/2 )

Now , dividing both of them to obtain the required value :

Tan ( a + b / 2 ) = 1/4 / ( 1/2 ) = 1/2

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