At least one of the answers above is NOT correct 6 pts If ta

At least one of the answers above is NOT correct (6 pts) If tan r--1/3, cosa > 0, sin 2x -6/5 cos 2x = 5/8 tan 2x=-3/4 then Note: You can earn partial credit on this problem.

Solution

We have given tanx=-1/3,cosx>0

secx=sqrt(1+tan²x)=sqrt(1+1/9)=sqrt(10)/3

cosx=1/secx =1/(sqrt(10)/3)=3/sqrt(10)

sinx=sqrt(1-cos²x)=sqrt(1-9/10)=-1/sqrt(10)

sin2x=2sinx*cosx=2*(-1/sqrt(10)) *3/sqrt(10) =-6/10=-3/5

sin2x=-3/5

cos2x=cos²x-sin²x=(3/sqrt(10))²-(-1/sqrt(10))² =(9/10)-1/10=8/10=4/5

cos2x=4/5

tan2x=2tanx/(1-tan²x)

=2*(-1/3)/(1-1/9)=(-2/3)/(8/9)=-2/3*9/8=-3/4

tan2x=-3/4