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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$\cos^2\frac{\pi}{12}+\cos^2\frac{\pi}{4}+\cos^2\frac{5\pi}{12}=$
  • A
    $\frac{2}{3+\sqrt{3}}$
  • B
    $\frac{2}{3}$
  • C
    $\frac{3+\sqrt{3}}{2}$
  • ✓
    $\frac{3}{2}$
✓

Answer

Correct option: D.
$\frac{3}{2}$
(D)
$\cos^7\frac{\pi}{12}+\cos^7\frac{\pi}{4}+\cos^7\frac{5\pi}{12}$
$=\cos^215^{\circ}+\cos^245^{\circ}+\cos^275^{\circ}$
$=\cos^215^{\circ}+\cos^275^{\circ}+\cos^245^{\circ}$
$=\cos^215^{\circ}+\sin^215^{\circ}+\left(\frac{1}{\sqrt{2}}\right)^2$
$\ldots\left[\because\cos^2\theta=\sin^2\left(90^{\circ}-\theta\right)\right]$
$=1+\frac{1}{2}$
$=\frac{3}{2}$

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