Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compounds1 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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