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2sin x+15cos^2 x=7then find tan x |
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Answer» 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 |
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