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if cosα=1/√2, sinβ=1/√3, show thattanα+β/2.cotα-β/2=5+2√6 or 5-2√6.
cos(a)=1/so, a=/4tan(a+b/2).cot(a-b/2)={sin(a+b/2).sin(a-b/2)}/{cos(a+b/2).cos(a-b/2)}{Sin(a+b/2+a-b/2)+sin(a+b/2+a-b/2)}/{sin(a+b/2+a-b/2)-sin(a+b/2-a+b/2)}{Sin(2a)+Sin(b)}/{Sin(2a)-sin(b)}On Putting a=/4,{Sin(/2)+Sin(b)}/{Sin(/2)-Sin(b)}For .. cos(b)= cos(b)= On putting this value. {1+}/{1-}On factorising We get The Proof.
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