- #1
ForceBoy
- 47
- 6
Homework Statement
The problem given is sin2(x) + tan2(x) = √2
2. Homework Equations
The relevant equations would be any trigonometric identities
The Attempt at a Solution
sin2(x) + tan2(x) = √2
sin2(x) + (sin2(x)/cos2(x) ) = √2
[ cos2(x) sin2(x) + sin2(x) ]/ cos2(x) = √2
[ (1- sin2(x)) sin2(x) + sin2(x)] / [ 1 - sin2(x) ] = √2
[ (2 - sin2(x) ) sin2(x) ] / [ 1 - sin2(x) ] = √2
(2 - sin2(x) ) tan2(x) = √2
tan2(x) = ( √2 / [ 2 - sin2(x) ] )
I take this and substitute into the first equation:
sin2(x) + ( √2 / [ 2 - sin2(x) ] ) = √2
( 2 - sin2(x) ) sin2(x) / [ 2 - sin2(x) ] + √2 / [ 2 - sin2(x) ] = √2
( 2 - sin2(x) ) sin2(x) + √2 / [ 2 - sin2(x) ] = √2
( 2 - sin2(x) ) sin2(x) + √2 = ( √2 ) 2 - sin2(x)
( 2 - sin2(x) ) sin2(x) + √2 = 2√2 - √2 sin2(x)
( 2 - sin2(x) ) sin2(x) = √2 - √2 sin2(x)
( 2 - sin2(x) ) sin2(x) = √2 (1 - sin2(x) )
( ( 2 - sin2(x) ) sin2(x) / (1 - sin2(x) ) )= √2Here 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.