Solve cosx+8sinx−7=0
My attempt:
8sinx=7−cosx⟹8⋅(2sinx2cosx2)=7−cosx⟹16sinx2cosx2=7−1+2sin2x2⟹16sinx2cosx2=6+2sin2x2⟹8sinx2cosx2=3+sin2x2⟹0=sin2x2−8sinx2cosx2+3⟹0=sinx2(sinx2−8cosx2)+3
I'm not sure how to proceed from here (if this process is even right at all?) . Any help would be appreciated. Thanks.
Answer
Divide either sides by cos2x2 sin2x2−8sinx2cosx2+3=0 to get tan2x2−8tanx2+3(1+tan2x2)=0 which on rearrangement is a Quadratic Equation in tanx2
No comments:
Post a Comment