Prove that cos-4-x-cos-4-x-2cosx-

As cos C+cos D=2cos(C+D2)cos(C D2) ⇒cos(π4+x)+cos(π4 x)=2cos(π4)cos(x)=2(1√(2))cos x =√(2)cos x . ...

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Formation of a Differential Equation from a General Solution

Prove that ...

Question

Prove that $cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) = \sqrt{2} cos x$ .

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Prove that cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) = \sqrt{2} cos x

(cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) - \sqrt{2} cos x)

(cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) + \sqrt{2} sin x)

cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) = \sqrt{2} cos x

Prove that

$(i) cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) = \sqrt{2} cos x$

(ii) $cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = - \sqrt{2} sin x$

cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) = - \sqrt{2} . cos x

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