Cos,Tan,Sin equations

1. Jun 20, 2010

pinnacleprouk

1. The problem statement, all variables and given/known data

sin x =√ 2 cos x

sin^2 x - cos^2 x - 2sin x = 1

Any help no matter how little is much appreciated

2. Relevant equations

3. The attempt at a solution

Not sure how to solve these,

2. Jun 20, 2010

danago

When solving these types of equations, one method is to try and use trigonometric identities to manupulate the equations so that only one type of trigonometric function is left.

For example, with the first one, what could you divide both sides by so that there is only sin, cos or tan left over?

3. Jun 20, 2010

HallsofIvy

Staff Emeritus
$$\frac{sin x}{cos x}= tan x= \sqrt{2}$$
Can you solve that?

Since $sin^2 x+ cos^2 x= 1$, $cos^2 x= 1- sin^2 x$ so this becomes
$$sin^2 x- (1- sin^2 x)- 2 sin x= sin^2 x- 1+ sin^2 x- 2sin x= 1$$
$$2sin^2 x- 2sin x- 2= 0$$
$$sin^2 x- sin x- 1= 0$$

Let y= sin x so the equation becomes $y^2- y- 1= 0$.