Trigonometric Functions — MATHS STD 11 Science — Question

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

Solution:

We have,

$2(1-2\sin^27​​\text{x})\sin3\text{x}=2(\cos14\text{x})\sin3\text{x}$ $[\because\cos2\text{x}=1-2\sin^2\text{x}]$

$=2\sin3\text{x}\cos14\text{x}$

$=\sin17\text{x}-\sin11\text{x}$ $[\because2\sin\text{A}\cos\text{xB}=\sin(\text{A+B})-\sin(\text{A}-\text{B})]$

$\therefore2(1-2\sin^27\text{x})\sin3\text{x}=\sin17\text{x}-\sin11\text{x}$