If cos A + cos B = p , sin A + sin B = q, and A-B= 2theta - Maths - Trigonometric Functions

Question

If cos A + cos B = p , sin A + sin B = q, and A-B= 2theta then
evaluate cos 3 theta / cos theta

Brijendra Pal · Accepted Answer

Dear Student,
cosA+cosB= p sinA+sinB= qSquaring and adding, sin2A+cos2A+sin2B+cos2B+2cosAcosB+sinAsinB= p2+q22cosA-B= p2+q2- 22cos2θ= p2+q2- 2Now, cos3θcosθ=4cos3θ-3cosθcosθ=4cos2θ-3= 2 p2+q2- 2-3= 2p2+2q2-7
Regards

If cos A + cos B = p , sin A + sin B = q, and A-B= 2theta .... then evaluate cos 3 theta / cos theta