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# Express the following as the sum difference of cosines and sines $2\cos 7\theta.\cos 3\theta$

$\begin{array}{1 1}(A)\;\cos 10\theta+\cos 7\theta\\(B)\;\cos 10\theta+\cos 4\theta\\(C)\;\cos 8\theta+\cos 7\theta\\(D)\;\text{None of these}\end{array}$

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A)
Toolbox:
• $2\cos A.\cos B=\cos(A+B)+\cos(A-B)$
$2\cos 7\theta.\cos 3\theta=\cos(7\theta+3\theta)+\cos(7\theta-3\theta)$
$\Rightarrow \cos 10\theta+\cos 4\theta$
Hence (B) is the correct answer.