Trigonometry

TRIGONOMETRIC FUNCTIONS : TRIGONOMETRIC FUNCTIONS

TRIGONOMETRIC IDENTITIES : TRIGONOMETRIC IDENTITIES Sin(A-B) = Sin A Cos B – Cos A Sin B Sin(A+B) = Sin A Cos B + Cos A Sin B Cos(A-B) = Cos A Cos B + Sin A Sin B Cos(A+B) = Cos A Cos B – Sin A Sin B Cos(p/2-x) = Sin x Cos(p/2+x) = - Sin x Cos(p±x) = -Cos x Sin(p+x) = -Sin x ; Sin(p-x) = Sin x Cos(2p-x) = Cos x Sin(2p-x) = Sin x

PROBLEM : PROBLEM 1.Prove Cos(p/4 – x). Cos(p/4 – y) – Sin (p/4 – x). Sin(p/4 – y) = Sin (x + y) Solution: Using 4th identity: LHS = Cos (p/4 – x + p/4 – y) = Cos (p/2 – (x + y)) = Sin (x + y)

PROBLEM : PROBLEM 2. Prove Cos(p/4 + x) + Cos(p/4 – x) = 2 3. Prove Cos 7x + Cos 5x + Cos 3x + Cos x = 4 Cos x Cos 2x Cos 4x 4. Sin 2x + 2 Sin 4x + Sin 6x = 4 cos2 x sin 4x