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Trigonometric Ratios Of Compound Angles — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Compound Angles1 Mark
Question
If $\sin\text{x}+\cos\text{x}=\text{a},$ find the value of $|\sin\text{x}-\cos\text{x}|.$
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Answer

$\sin+\cos\text{x}=\text{a}$
squaring on both sides gives
$\sin^2\text{x}+\cos^2\text{x}+2\sin\text{x}\cos\text{x}=\text{a}^2$
$1+\sin2\text{x}=\text{a}^2$
$\sin2\text{x}=\text{a}^2-1$
If $\sin2\text{x}=\text{a}^2-1.$ then
$(\sin2\text{x}=\text{a}^2)=\sin^2\text{x}+\cos^2\text{x}-2\sin\text{x}\cos\text{x}=1(\text{a}^2-1)=2-\text{a}^2$
Take square root on both side, we get
$|\sin\text{x}-\cos\text{x}|=\sqrt{2-\text{a}^2}$

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