Question

2sin x+15cos^2 x=7then find tan x​

Answer 1

Answer

sin²x+cos²x =1 (identity)

cos²x = 1-sin²x

2sinx +15cos²x =7

put 1-sin²x instead of cos²x

2sinx +15(1-sin²x) =7

-15sin²x +2sinx +8=0 => (form of a quadratic equation)

sina =t

-15t² +2t +8=0

t= 4/5 and t = -2/3 => (after using quadratic formula)

t = 4/5 is the real solution (the other one makes a negative angle)

sinx= 4/5

sin²x = 16/25 => (after squaring both sides)

remember identity sin²a+cos²a=1 => sin²a = 1-cos²a

1-cos²x =16/25 => cos²x=9/25 => cosx =3/5 ( the other solution -3/5 makes negative angle)

tanx = sinx / cosx = > (4/5) /(3/5) = 4/3