- #1

- 47

- 6

## Homework Statement

The problem given is

2. Homework Equations

*sin*

^{2}(x) + tan^{2}(x) = √22. Homework Equations

The relevant equations would be any trigonometric identities

## The Attempt at a Solution

sin

^{2}(x) + tan

^{2}(x) = √2

sin

^{2}(x) + (sin

^{2}(x)/cos

^{2}(x) ) = √2

[ cos

^{2}(x) sin

^{2}(x) + sin

^{2}(x) ]/ cos

^{2}(x) = √2

[ (1- sin

^{2}(x)) sin

^{2}(x) + sin

^{2}(x)] / [ 1 - sin

^{2}(x) ] = √2

[ (2 - sin

^{2}(x) ) sin

^{2}(x) ] / [ 1 - sin

^{2}(x) ] = √2

(2 - sin

^{2}(x) ) tan

^{2}(x) = √2

tan

^{2}(x) = ( √2 / [ 2 - sin

^{2}(x) ] )

I take this and substitute into the first equation:

sin

^{2}(x) + ( √2 / [ 2 - sin

^{2}(x) ] ) = √2

( 2 - sin

^{2}(x) ) sin

^{2}(x) / [ 2 - sin

^{2}(x) ] + √2 / [ 2 - sin

^{2}(x) ] = √2

( 2 - sin

^{2}(x) ) sin

^{2}(x) + √2 / [ 2 - sin

^{2}(x) ] = √2

( 2 - sin

^{2}(x) ) sin

^{2}(x) + √2 = ( √2 ) 2 - sin

^{2}(x)

( 2 - sin

^{2}(x) ) sin

^{2}(x) + √2 = 2√2 - √2 sin

^{2}(x)

( 2 - sin

^{2}(x) ) sin

^{2}(x) = √2 - √2 sin

^{2}(x)

( 2 - sin

^{2}(x) ) sin

^{2}(x) = √2 (1 - sin

^{2}(x) )

( ( 2 - sin

^{2}(x) ) sin

^{2}(x) / (1 - sin

^{2}(x) ) )= √2

Here is where I get stuck. I do not know what steps to take next. Please give me hints on this and do not hesitate to point out any mistakes in my work. They are very likely.