If sin x-cos x-2cos x- then cos x-sin x is equal to

The correct option is D cos x + sin x = √(2)cos x sin x = ( √(2) 1)cos x cos x = 1/( √(2) 1)sin x cos x = ( √(2) + 1)sin x cos x sin x = √(2)sin x ...

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Standard XII

Mathematics

Integration by Substitution

If sin x+cos ...

Question

If $sin x + cos x = \sqrt{2} cos x$ , then cosx - sin x is equal to

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Solution

The correct option is C
$cos x + sin x = \sqrt{2} cos x$
$sin x = (\sqrt{2} - 1) cos x$
$cos x = \frac{1}{(\sqrt{2} - 1)} sin x$
$cos x = (\sqrt{2} + 1) sin x$
$cos x - sin x = \sqrt{2} sin x$

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If sinx+cosx=√2cosx, then cosx - sin x is equal to

The correct option is C cosx+sinx=√2cosx sinx=(√2−1)cosx cosx=1(√2−1)sinx cosx=(√2+1)sinx cosx−sinx=√2sinx

If $sin x + cos x = \sqrt{2} cos x$ , then cosx - sin x is equal to

The correct option is C
$cos x + sin x = \sqrt{2} cos x$
$sin x = (\sqrt{2} - 1) cos x$
$cos x = \frac{1}{(\sqrt{2} - 1)} sin x$
$cos x = (\sqrt{2} + 1) sin x$
$cos x - sin x = \sqrt{2} sin x$