formulae sin (A B) = sinAcosB cosAsinB cos (A B) = cos AcosB sinAsinB tan (A B) =
tan A tan B 1 tan A tan B
Half-angle formulae sin2A = 2 sinA cosA cos 2A = cos2A – sin2 A = 2 cos2A-1 = 1- 2 sin2A tan 2A =
sinA = 2 sin
A A cos 2 2
cos A = cos2
A A – sin2 2 2 A -1 2 A = 1- 2 sin2 2
2 tan A 1 tan 2 A
= 2 cos2
A 2 tan A = 2 A 1 tan 2 2 tan
Exercises: 1. Prove the following trigonometric functions. cos( x y) (a) 1 tan x tan y cos x cos y (b) sin 4 x 4 sin x cos3 x 4 sin 3 x cos x 7 3 and sin B = - , and the angles A and B are in the first and 25 5 third quadrant. Find the value of tan (A+B). 12 4 3. Given that sin A= cos B= and the angles A and B in the 2nd and 4th 13 5 quadrants. Find the value of cos (A-B). 24 4. Given that cos without using ,0 90, find the value of sin 25 2 calculator. 12 5. Given that tan ,90 180, find the value of cos without using 5 2 calculator.
2. Given that sin A=
1
Prepared by: Pn shila smkdp 2013