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Homework Help
Precalculus Mathematics Homework Help
How Do You Solve sin^2(x) + tan^2(x) = √2?
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[QUOTE="ForceBoy, post: 6020161, member: 641863"] [h2]Homework Statement [/h2] The problem given is [B][I]sin[SUP]2[/SUP](x) + tan[SUP]2[/SUP](x) = √2 [/I] 2. Homework Equations [/B] The relevant equations would be any trigonometric identities [h2]The Attempt at a Solution[/h2] [I][/I] sin[SUP]2[/SUP](x) + tan[SUP]2[/SUP](x) = √2 sin[SUP]2[/SUP](x) + (sin[SUP]2[/SUP](x)/cos[SUP]2[/SUP](x) ) = √2 [ cos[SUP]2[/SUP](x) sin[SUP]2[/SUP](x) + sin[SUP]2[/SUP](x) ]/ cos[SUP]2[/SUP](x) = √2 [ (1- sin[SUP]2[/SUP](x)) sin[SUP]2[/SUP](x) + sin[SUP]2[/SUP](x)] / [ 1 - sin[SUP]2[/SUP](x) ] = √2 [ (2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) ] / [ 1 - sin[SUP]2[/SUP](x) ] = √2 (2 - sin[SUP]2[/SUP](x) ) tan[SUP]2[/SUP](x) = √2 [B][B][B][B][B][B][B][B][B][B][B][B][B][B][/B][/B][/B][/B][/B][/B][/B][/B][/B][/B][/B][/B][/B][/B] tan[SUP]2[/SUP](x) = ( √2 / [ 2 - sin[SUP]2[/SUP](x) ] ) I take this and substitute into the first equation: sin[SUP]2[/SUP](x) + ( √2 / [ 2 - sin[SUP]2[/SUP](x) ] ) = √2 ( 2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) / [ 2 - sin[SUP]2[/SUP](x) ] + √2 / [ 2 - sin[SUP]2[/SUP](x) ] = √2 ( 2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) + √2 / [ 2 - sin[SUP]2[/SUP](x) ] = √2 ( 2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) + √2 = ( √2 ) 2 - sin[SUP]2[/SUP](x) ( 2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) + √2 = 2√2 - √2 sin[SUP]2[/SUP](x) ( 2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) = √2 - √2 sin[SUP]2[/SUP](x) ( 2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) = √2 (1 - sin[SUP]2[/SUP](x) ) ( ( 2 - sin[SUP]2[/SUP](x) ) sin[SUP]2[/SUP](x) / (1 - sin[SUP]2[/SUP](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. [/QUOTE]
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Precalculus Mathematics Homework Help
How Do You Solve sin^2(x) + tan^2(x) = √2?
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