How do you solve 4sinxcosx=14sinxcosx=1?

1 Answer

x=pi/12+kpx=π12+kpi,
x = (5pi)/12+kpix=5π12+kπ

Explanation:

Use the trig identity:
sin 2x = 2sin xcos xsin2x=2sinxcosx
In this case,
4sin xcos x = 2sin 2x = 14sinxcosx=2sin2x=1 =>
sin 2x = 1/2sin2x=12
Trig table and unit circle give 2 solutions:
a. 2x=pi/6 + 2kpi2x=π6+2kπ -->
x=pi/12 + kpix=π12+kπ.
b. 2x=(5pi)/6 + 2kpi2x=5π6+2kπ, -->
x=(5pi)/12 + kpix=5π12+kπ.