Question

if sin theta 1 + sin theta 2 + sin theta is equal to 3 then find the value of cos theta + cos theta 2 + cos theta 3​

Answer 1

Given (2 cosθ - sinθ) = x   and (cosθ - 3 sinθ) = y 

Put the values of x and y in 2x2 + y2 − 2xy (LHS) 

= 2(2 cosθ − sinθ)2 + (cosθ − 3 sinθ)2 − 2(2 cosθ − sinθ)(cosθ − 3 sinθ) 

= 2(4cos2θ − 4cosθ sinθ + sin2θ) + (cos2θ − 6cosθ sinθ + 9sin2θ) − 2(2cos2θ − 7cosθ sinθ + 3sin2θ) 

= 8cos2θ − 8cosθ sinθ + 2sin2θ + cos2θ − 6cosθ sinθ + 9sin2θ − 4cos2θ + 14cosθ sinθ − 6sin2θ 

= 5cos2θ + 5sin2θ 

= 5(cos2θ + sin2θ) 

= 5(1) = 5        (Since cos2θ + sin2θ = 1)

=RHS