Question

Using the formula, cos A = `sqrt((1+cos2A)/2) ,`find the value of cos 30⁰, it being given that cos 60⁰  = `1/2`.

Answer 1

A = 300
⇒ 2A = 2 × 30⁰ = 60⁰ 
By substituting the value of the given T-ratio, we get:

cos A = `sqrt((1+ cos^2A)/2)`

cos `30^0 = sqrt((1+cos 60^0)/2) = sqrt((1+(1/2)/2)) = sqrt((3/2)/2) =sqrt(3/4) = sqrt(3)/2`

∴ cos A = `sqrt(3)/2`