Prove that- cos3-4-x -cos3-4-x -2sin x

Cos( 3 π4 +x ) cos( 3 π4 x ) = √(2)sin x Let A= 3 π4+ x, B = 3 π4 x ⇒ L.H.S = 2 sin((3π4+x)+(3π4 x )2) sin((3π4+x ) (3π4 x )2) = 2 sin(3π4) sin (x)= 2 sin ...

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Standard XII

Physics

Introduction

Prove that: c...

Question

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

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Solution

$cos (\frac{3 π}{4} + x) - cos (\frac{3 π}{4} - x) = - \sqrt{2} sin x$
Let $A = \frac{3 π}{4} + x, B = \frac{3 π}{4} - x$

$\Rightarrow L . H . S = - 2 sin ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ \frac{(\frac{3 π}{4} + x) + (\frac{3 π}{4} - x)}{2} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ sin ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ \frac{(\frac{3 π}{4} + x) - (\frac{3 π}{4} - x)}{2} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠$
$= - 2 sin (\frac{3 π}{4}) sin (x) = - 2 sin (π - \frac{π}{4}) sin (x) = - 2 sin \frac{π}{4} \cdot sin x = - \sqrt{2} sin x$
$∴ L . H . S . = R . H . S .$
Hence proved.

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Similar questions

Q. Prove the following:

c o s (\frac{3 π}{4} + x) - c o s (\frac{3 π}{4} - x) = - \sqrt{2} s i n x

Prove that

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

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

Q. Find

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

Q. If

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

.Find

m

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Introduction

Standard XII Physics

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Prove that: cos(3π4+x)−cos(3π4−x)=−√2sinx

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