If A = 30 and B = 60, verify that

cos(A + B) = cosA cosB – sinA sinB

If α is measure of acute angle and 3sinα = 2cosα, prove that

If A = 30 and B = 60, verify that

sin(A + B) = sinA cosB + cosA sinB,

If sin(A – B) = sinA cosB – cosA sinB and cos(A – B) = cosA cosB + sinA sinB, find the values of sin15 and cos15.

State whether the following are true or false. Justify your answer:

(1) The value of sinθ increases as θ increases from 0 to 90.

(2) sinθ = cosθ for all value ofθ.

(3) cos(A + B) = cosA + cosB

(4) tanA is not defined for A = 90.

(5) The value of cot increases as θ increases from 0 to 90.