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Cosine Rule

Prove that co...

Question

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

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Solution

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

L. H. S. = $cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x)$

$cos (A + B) + cos (A - B) = 2 cos A cos B$

$= 2 cos (\frac{π}{4}) c o s x$

$= 2 \frac{1}{\sqrt{2}} \times cos x$

$= \sqrt{2} cos x = R . H . S$

Hence proved.

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

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

State the whether given equation is true or false

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

Prove that

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

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

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