Prove that the equation is an identity. State any restrictions.

[goracheski]

Homework Statement

cos(x)^2/(1+3sin(x)-4sin(x)^2)=(1+sin(x))/(1+4sin(x))

Homework Equations

We are taking a topic in math where you rearrange one side of the formula to match the other

The Attempt at a Solution

I have factor 1+3sin(x)-4sin(x)^2 to get (-sin(x)+1)(4sin(x)+1)

 

[jedishrfu]

if you rewrite 1 + 3 sin x -4 (sin x)^2 using u-sin x you get the quadratic - 4 u^2 + 3u +1 which is fairly easy to factor.

 

[Mark44]

Homework Statement

cos(x)^2/(1+3sin(x)-4sin(x)^2)=(1+sin(x))/(1+4sin(x))

Homework Equations

We are taking a topic in math where you rearrange one side of the formula to match the other

The Attempt at a Solution

I have factor 1+3sin(x)-4sin(x)^2 to get (-sin(x)+1)(4sin(x)+1)

Continue working on the left side of your equation. What can you do with cos²(x). There's an identity you can use to change it.

The factors you found for the denominator are correct, but it would be better to write them as (1 - sin(x))(1 + 4sin(x)).