Question

prove that cos theta × cos theta/2 - cos 3 theta × cos 9 theta/2 = sin 7 theta × sin 8 theta​

Answer 1

Answer:

Answer Text

Solution :

LHS = cosθcosθ2−cos3θcos9θ2  

=12[2cosθ⋅cosθ2−2cos3θ⋅cos9θ2]  

=12[cos(θ+θ2)+cos(θ−θ2)−cos(3θ+9θ2)−cos(3θ−9θ2)]  

12(cos3θ2+cosθ2−cos15θ2−cos3θ2  

=12[cosθ2−cos15θ2]  

=−12[2sin(θ+15θ2)⋅sin(θ−15θ2)] [∵cosx−cosy=−2sinx+y2⋅sinx−y2]  

=+(sin8θ⋅sin7θ)=RHS  

∴ LHS=RHS  Hence proved.

Step-by-step explanation:

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