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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
Let $B =2 \sin ^2 x-\cos 2 x$, then
  • ✓
    $-1 \leq B \leq 3$
  • B
    $0 \leq B \leq 2$
  • C
    $-1 \leq B \leq 1$
  • D
    $-2 \leq B \leq 2$
✓

Answer

Correct option: A.
$-1 \leq B \leq 3$
(A)
$2 \sin ^2 x-\cos 2 x=4 \sin ^2 x-1$ and $0 \leq \sin ^2 x \leq 1 \Leftrightarrow 0 \leq 4 \sin ^2 x \leq 4$
$\Rightarrow-1 \leq 4 \sin ^2 x-1 \leq 3$

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