# Cos,Tan,Sin equations

## Homework Statement

sin x =√ 2 cos x

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

Any help no matter how little is much appreciated

## The Attempt at a Solution

Not sure how to solve these,

danago
Gold Member
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?

HallsofIvy
Homework Helper

## Homework Statement

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

sin^2 x - cos^2 x - 2sin x = 1
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 $y^2- y- 1= 0$.

Any help no matter how little is much appreciated

## The Attempt at a Solution

Not sure how to solve these,