5. Find the maximum value of a cos theta+b sin (theta+alpha) (a,beta,theta are constants.)

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z = α sin θ + β cos θ

α

β

z

cos α + cos β = a, sin α + sin β = b, α - β = 2 θ

\frac{cos 3 θ}{cos θ}

a sin (θ + α) = b sin (θ + β)

cot θ = \frac{a cos α - b cos β}{b sin β - a sin α}

cosα+cosβ=a, sinα+sinβ=b and α-β = 2θ. If $\frac{c o s 3 θ}{c o s θ}$ = K, when a= $\frac{1}{3}$ ,b= $\frac{1}{2}$ Find the value of

-36K.

cos (α - θ) = a

cos (β - θ) = b

{sin}^{2} (α - β) + 2 a b cos (α - β)

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