to solve the equation 5sin(2x) = 3cosx, you should rewrite it as _____. a. cosx(5sinx - 3) = 0 b. 5sinx +…
to solve the equation 5sin(2x) = 3cosx, you should rewrite it as _____. a. cosx(5sinx - 3) = 0 b. 5sinx + 3cosx = 0 c. cosx(10sinx - 3) = 0
Answer
Answer:
C. $\cos x(10\sin x - 3)=0$
Explanation:
Step1: Use double - angle formula
Recall $\sin(2x)=2\sin x\cos x$. So $5\sin(2x)=5\times2\sin x\cos x = 10\sin x\cos x$.
Step2: Rewrite the original equation
The original equation $5\sin(2x)=3\cos x$ becomes $10\sin x\cos x=3\cos x$.
Step3: Rearrange the equation
Subtract $3\cos x$ from both sides: $10\sin x\cos x - 3\cos x=0$.
Step4: Factor out $\cos x$
Factor out $\cos x$ from the left - hand side: $\cos x(10\sin x - 3)=0$.