Given that (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2) = 7, show that tan(x)^2 = 3/2
First, we use 1 - sin(x)^2 = cos(x)^2 and get:(LHS) (cos(x)^2 + 4 sin(x)^2)/(1-sin(x)^2)= (cos(x)^2 + 4 sin(x)^2)/cos(x)^2= 1 + 4 (sin(x)/cos(x))^2= 1 + 4 tan(x)^2Now we know that the left hand side is equal to 7.Hence, 1 + 4 tan(x)^2 = 7 <=> tan(x)^2 = 3/2
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