Question

Verify : sin60 = 2tan30/1+tan²30

Answer 1

(2 tan 30)/(1+tan^2 30) = sin 60? 

LHS = (2 tan 30)/(1+tan^2 30) 
= (2tan30)/ (1+ sin^2 30/ cos^2 30) 
= (2tan30)/ (sin^2 30 + Cos^2 30)/ cos ^2 30 
= (2tan30) / (1/cos^2 30) [Because sin^2 theta + cos^2 theta =1] 
= 2tan30*cos^2 30/1 
= (2sin30/cos30) *cos^2 30 
= 2sin 30* cos 30 [ because 2(sin theta) * (Cos theta) = sin 2 theta ) 
= sin 2*30 
= sin60 = RHS proved. Thank you.

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