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Principal Solution of Trigonometric Equation

Find the valu...

Question

Find the value of $(cos x - sin x)^{2}$ , if the product $cos x sin x = 0.22$ .

0

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0.11

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0.44

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0.56

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1.00

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Solution

The correct option is D $0.56$
Given, $cos x sin x = 0.22$
Therefore, the value of ${(cos x - sin x)}^{2}$
$= {cos}^{2} x + {sin}^{2} x - 2 sin x cos x$
$= 1 - 2 \times 0.22$
$= 0.56$

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