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if cosα=1/√2, sinβ=1/√3, show that tanα+β/2.cotα-β/2=5+2√6 or 5-2√6.

if cosα=1/√2, sinβ=1/√3, show that
tanα+β/2.cotα-β/2=5+2√6 or 5-2√6.

Grade:12th pass

1 Answers

Kuldeep Pal
53 Points
7 years ago
cos(a)=1/\sqrt{2}
so, a=\pi/4
tan(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=\pi/4,
{Sin(\pi/2)+Sin(b)}/{Sin(\pi/2)-Sin(b)}
For .. cos(b)=\sqrt{1-sin^{2}(b)}
     cos(b)= \sqrt{2/3}
On putting this value.
       {1+\sqrt{2/3}}/{1-\sqrt{2/3}}
On factorising We get The Proof.

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