Question 1192632: Find sin(2x), cos(2x), and tan(2x) from the given information.
csc(x) = 8, tan(x) < 0 Found 2 solutions by mananth, ikleyn:Answer by mananth(16946) (Show Source): You can put this solution on YOUR website! csc(x)=8 Given)
⇒sinx=1/8
cos^2x=1−sin^2x
⇒cos^2x=1−1/64=63/64
⇒cosx=3√7/8
1. sin2x=2sinxcosx
sin2x=2×18×3√78
sin2x=3√732
2. cos2x=2cos^2x−1
cos2x=(2×63/64)−1
cos2x=(63/32)
3. tan2x=sin2xcos2x
tan2x=3√7/31
The solution by @mananth is elementary wrong.
I came to bring a correct soluition.
You are given that csc(x) = 8, tan(x) < 0.
It means that sin(x) = , tan(x) < 0; hence x is the angle in QII, second quadrant.
It implies that cos(x) = = = = .
Now sin(2x) = 2*sin(x)*cos(x) = = ;
cos(2x) = cos^2(x) - sin^2(x) = - = = .
tan(2x) = = .