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

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compound Angles1 Mark
Question
If $\frac{\pi}{4}<\text{x}<\frac{\pi}{2},$ then write the value of $\sqrt{1-\sin2\text{x}}$
✓

Answer

Since, $\frac{\pi}{4}<\theta<\frac{\pi}{2}\Rightarrow\theta$ lies in the first quadrant 1st quadarant
Now,
$\sqrt{1-\sin2\theta}=\sqrt{\sin^2\theta+\cos^2\theta-2\sin\theta}$
$=\sqrt{(\sin\theta-\cos\theta)^2}$
$=\sin\theta-\cos\theta$

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