Target Mathematics

1.101: Trigonometric identities

4PM1/2/January/2016 — Question 6 · 6 marks

sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B\sin(A+B)=\sin A\cos B+\cos A\sin B
cos⁡(A+B)=cos⁡Acos⁡B−sin⁡Asin⁡B\cos(A+B)=\cos A\cos B-\sin A\sin B
sin⁡Acos⁡A=tan⁡A\dfrac{\sin A}{\cos A}=\tan A
Using the above formulae, show that
(a) sin⁡2x=2sin⁡xcos⁡x\sin2x=2\sin x\cos x (1)
(b) cos⁡2x=cos⁡2x−sin⁡2x\cos2x=\cos^2x-\sin^2x (1)
(c) sin⁡2x1+cos⁡2x=tan⁡x\dfrac{\sin2x}{1+\cos2x}=\tan x (4)