Prove that, (i) cos α+cos β+cos γ+cos(α+β+γ)=4 cos(α+β2). cos(

1.	Prove that, (i) cos α+cos β+cos γ+cos(α+β+γ)=4 cos(α+β2). cos(β+γ2). cos(γ+α2). (ii) If tan x=ba, then √a+ba−b+√a−ba+b=2 cos x√cos 2x.
Answer» Prove that, (i) $c o s α + c o s β + c o s γ + c o s (α + β + γ) = 4 c o s (\frac{α + β}{2}) . c o s (\frac{β + γ}{2}) . c o s (\frac{γ + α}{2}) .$ (ii) If $t a n x = \frac{b}{a},$ then $\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}} = \frac{2 c o s x}{\sqrt{c o s 2 x}} .$

Prove that, (i) cos α+cos β+cos γ+cos(α+β+γ)=4 cos(α+β2). cos(β+γ2). cos(γ+α2). (ii) If tan x=ba, then √a+ba−b+√a−ba+b=2 cos x√cos 2x.

Answer»

Prove that,

(i) $c o s α + c o s β + c o s γ + c o s (α + β + γ) = 4 c o s (\frac{α + β}{2}) . c o s (\frac{β + γ}{2}) . c o s (\frac{γ + α}{2}) .$

(ii) If $t a n x = \frac{b}{a},$ then $\sqrt{\frac{a + b}{a - b}} + \sqrt{\frac{a - b}{a + b}} = \frac{2 c o s x}{\sqrt{c o s 2 x}} .$