Problem: If sinx+cosx=1/5 and 0⩽x<π, then tanx is
Answer Choices:
A. −34
B. −43
C. 43
D. 34
E. not completely determined by the given information
Solution:
If sinx+cosx=51, then
1−sin2x=cos2x=(51−sinx)225sin2x−5sinx−12=0
Similarly, cosx satisfies the equation 25t2−5t−12=0, whose solutions are 54 and −53. Since sinx⩾0,sinx=54; and sincecosx=51−sinx, cosx=−53. Hence, tanx=−34.