Question

2sinx+15cos^2x=7 find cotx

Answer 1

Answer:

i have replaced x as 'a'

Step-by-step explanation:

cos²a = 1-sin²a  

2sina +15cos²a =7  

put 1-sin²a instead of cos²a  

2sina +15(1-sin²a) =7  

-15sin²a +2sina +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)  

sina= 4/5  

sin²a = 16/25 => (after squaring both sides)  

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

1-cos²a =16/25 => cos²a =9/25 => cosa =3/5 ( the other solution -3/5 makes negative angle)  

cota = cosa / sina = > (3/5) / (4/5) = 3/4

Answer 2

2sinx+15 (1-sin^2x)=7
2sinx-15sin^2x=-8
15sin^2x-2sinx-8=0
sinx=t
15 (t^2)-2 (t)-8=0