Express each of the following as a function of a single angl

Express each of the following as a function of a single angle and evaluate. sin 60 degree cos 30 degree + cos 60 degree sin 30 degree cos 60 degree cos 30 degree - Sin 60 degree sin 30 degree 2 sin 30 degree cos 30 degree tan 20 degree + tan 25 degree/1 - tan 20 degree tan 25 degree Given that sin theta = 3/5 and cos theta = 4/5, where 0

Solution

8. (tan 20 + tan 25)/(1- tan 20 tan 25)

tan(A+B) = (tan A + tan B)/(1- tan A tan B)

Using the above formula we get

tan(20+25) = tan 45 = 1

9. sin theta=3/5   and cos theta =4/5

SIn 2 theta = 2sin theta cos theta =2 (3/5)(4/5)= 24/25

sin 2 theta=24/25

10. cos 2 theta = cos²theta - sin²theta = (4/5)²-(3/5)²= 7/25

cos 2 theta = 7/25