Move <span><span>5cos<span>(x)</span></span><span>5cos<span>(x)</span></span></span> to the left side of the equation by subtracting it from both sides.<span><span>5sin<span>(2x)</span>−5cos<span>(x)</span>=0</span><span>5sin<span>(2x)</span>-5cos<span>(x)</span>=0</span></span>Simplify each term.Apply the sine double-angle identity.<span><span>5<span>(2sin<span>(x)</span>cos<span>(x)</span>)</span>−5cos<span>(x)</span>=0</span><span>5<span>(2sin<span>(x)</span>cos<span>(x)</span>)</span>-5cos<span>(x)</span>=0</span></span>Multiply <span>22</span> by <span>55</span> to get <span>1010</span>.<span><span>10<span>(sin<span>(x)</span>cos<span>(x)</span>)</span>−5cos<span>(x)</span>=0</span><span>10<span>(sin<span>(x)</span>cos<span>(x)</span>)</span>-5cos<span>(x)</span>=0</span></span>Remove parentheses around <span><span>sin<span>(x)</span>cos<span>(x)</span></span><span>sin<span>(x)</span>cos<span>(x)</span></span></span>.<span><span>10sin<span>(x)</span>cos<span>(x)</span>−5cos<span>(x)</span>=0</span><span>10sin<span>(x)</span>cos<span>(x)</span>-5cos<span>(x)</span>=0</span></span>Factor <span><span>5cos<span>(x)</span></span><span>5cos<span>(x)</span></span></span> out of <span><span>10sin<span>(x)</span>cos<span>(x)</span>−5cos<span>(x)</span></span><span>10sin<span>(x)</span>cos<span>(x)</span>-5cos<span>(x)</span></span></span>. Factor <span><span>5cos<span>(x)</span></span><span>5cos<span>(x)</span></span></span> out of <span><span>10sin<span>(x)</span>cos<span>(x)</span></span><span>10sin<span>(x)</span>cos<span>(x)</span></span></span>.<span><span>5cos<span>(x)</span><span>(2sin<span>(x)</span>)</span>−5cos<span>(x)</span>=0</span><span>5cos<span>(x)</span><span>(2sin<span>(x)</span>)</span>-5cos<span>(x)</span>=0</span></span>Factor <span><span>5cos<span>(x)</span></span><span>5cos<span>(x)</span></span></span> out of <span><span>−5cos<span>(x)</span></span><span>-5cos<span>(x)</span></span></span>.<span><span>5cos<span>(x)</span><span>(2sin<span>(x)</span>)</span>+5cos<span>(x)</span><span>(−1)</span>=0</span><span>5cos<span>(x)</span><span>(2sin<span>(x)</span>)</span>+5cos<span>(x)</span><span>(-1)</span>=0</span></span>Factor <span><span>5cos<span>(x)</span></span><span>5cos<span>(x)</span></span></span> out of <span><span>5cos<span>(x)</span><span>(2sin<span>(x)</span>)</span>+5cos<span>(x)</span>⋅−1</span><span>5cos<span>(x)</span><span>(2sin<span>(x)</span>)</span>+5cos<span>(x)</span>⋅-1</span></span>.<span>5cos<span>(x)</span><span>(2sin<span>(x)</span>−1)</span>=<span>0</span></span>
sin 4x = 2sin 2x.cos 2x 10sin 2x.cos 2x + 10sin 2x = 0 10sin 2x(cos 2x + 1) = 0 a. sin 2x = 0 --> 2x = 0 --> x = 0 2x = pi --> x = pi/2 2x = 2pi x = pi b. cos 2x = -1 --> 2x = pi --> x = pi/2
