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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $A =133^{\circ}$, then $2 \cos \frac{A}{2}$ is equal to
  • A
    $-\sqrt{1+\sin A}-\sqrt{1-\sin A}$
  • B
    $-\sqrt{1+\sin A }+\sqrt{1-\sin A }$
  • ✓
    $\sqrt{1+\sin A }-\sqrt{1-\sin A }$
  • D
    $\sqrt{1+\sin A }+\sqrt{1-\sin A }$
✓

Answer

Correct option: C.
$\sqrt{1+\sin A }-\sqrt{1-\sin A }$
(C)
For $A =133^{\circ}, \frac{ A }{2}=66.5^{\circ}$
$\Rightarrow \sin \frac{ A }{2}>\cos \frac{ A }{2}>0$
$\sqrt{  1+\sin A} =\sin \frac{ A }{2}+\cos \frac{ A }{2} \quad\ldots(i)$
and $\sqrt{1-\sin A }=\sin \frac{ A }{2}-\cos \frac{ A }{2}\quad\ldots(ii)$
Subtracting (ii) from (i), we get
$2 \cos \frac{A}{2}=\sqrt{1+\sin A }-\sqrt{1-\sin A }$

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