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

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Ratios Of Compound Angles1 Mark
Question
If $\frac{\pi}{2}<​\text{x}<\frac{3\pi}{2},$ then write the value of $\sqrt{\frac{1+\cos2​\text{x}}{2}}$
✓

Answer

Since $\frac{\pi}{2}<\theta<\frac{3\pi}{2}\Rightarrow2^{\text{nd}}\ \&\ 3^{\text{rd}}$ quadarant
Now,
$\sqrt{\frac{1+\cos2\theta}{2}}=\sqrt{\frac{2\cos^2\theta}{2}}$
$-\cos\theta (-ve$ sigh due to $2^{nd}\ 3^{rd}$ quad$)$
$=-\cos\theta$

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