For what value of x does cos^2(x) = 3sin^2(x)

Answer 1

Use the identity cos^2 x = 1-sin^2 xwhich gives you

1-sin^2 x= 3sin^2 x

1= 4sin^2x

sin^2 x = 1/4 Take the square root of both sides to solve for sin x

sin x = square root 1/4 =

So what angles have a sin of 1/2 That would be 30 degrees ( pi/6) and 150 degrees ( 5pi/6)

Solutions are then p/6 + 2(pi)n. And 5pi/6 +2(pi)n

Answer 2

This equation is equivalent to tan²x = 1/3 and to tan x = sqrt(1/3)

tan²x is periodic with period π; that means there will be infinitely many answers, one of which is π/6.