2(1-2 ^27x) 3x is equal to: - Vidyadip

MCQ

$2(1-2\sin^27\text{x})\sin3\text{x}$ is equal to:

✓
$\sin17\text{x}-\sin11\text{x}$
B
$\sin11\text{x}-\sin17\text{x}$
C
$\cos17\text{x}-\cos11\text{x}$
D
$\cos17\text{x}+\cos11\text{x}$

✓

Answer

Correct option: A.

$\sin17\text{x}-\sin11\text{x}$

We have,
$2(1-2\sin^27\text{x})\sin3\text{x}=2(\cos14\text{x})\sin3\text{x}$ $[\because\cos2\text{x}=1-2\sin^2\text{x}]$
$=2\sin3\text{x}\cos14\text{x}$
$=\sin17\text{x}-\sin11\text{x}$ $[\because2\sin\text{A}\cos\text{xB}=\sin(\text{A+B})-\sin(\text{A}-\text{B})]$
$\therefore2(1-2\sin^27\text{x})\sin3\text{x}=\sin17\text{x}-\sin11\text{x}$

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