Question
(i) Prove that cos (α + β) )= cos α cos β – sin α sin β.
(ii) Prove that cos (α – p) = cos α cos β + sin α sin β.
Solution
(i) Draw a circle with centre at O and radius = 1.
Let P, Q be two points on the circle such that
∠POX = α and ∠QQX = β.
∴ ∠POQ = α + β
Co-ordinates of P, Q are (cos α, sin α) and (cos β, – sin β) respectively.
(ii) Draw a circle with centre at O and radius = 1.
Let P, Q be two points on the circle such that
∠POX = α, ∠QOX = β
∴ ∠POQ = α – β
Co-ordinates of P, Q are (cos α, sin α) and (cos β, sin β) respectively.
