Answer :

Given,


cos θ = 8/17


sin θ = ±√(1 – cos2θ)


But θ lies in first quadrant, so only positive sign is considered.


sin θ = √( 1 – 64/289) = 15/17


Let, y = cos(30° + θ) + cos (45° – θ) + cos (120° – θ)


We know that: cos(x + y) = cos x cos y – sin x sin y


y = cos30° cos θ – sin30° sin θ + cos45° cos θ + sin45°sin θ +cos120° cos θ + sin120° sin θ


Putting values of cos30° ,sin30° ,cos 120° ,sin120° and cos 45°






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