Answer to Question #139923 in Trigonometry for Michael

Question

Use a double angle formula to rewrite each trigonometric ratio

a) sin (4a)
b) cos (6a)
c) tan (5a)

Answer 1

(a) Sin(4a)=$Sin2(2a)=2sin2acos2a$

Further It can be resolved as

=$2\times 2sinacosa\times (2cos^2a-1)$

=$8sinacos^3a-4sinacosa$

(b) Cos(6A)=cos2(3a)=2$cos^23a-1$ or $1-2sin^23a$

(c) tan(5a)=tan2(2.5a)=$\dfrac{2tan(2.5a)}{1-tan^22.5a}$