anonymous
  • anonymous
prove the identity that (tan^2 x) - (sin^2 x) = (tan^2 x)(sin^2 x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Shayaan_Mustafa
  • Shayaan_Mustafa
candy020202 are you here?
anonymous
  • anonymous
yeah
Shayaan_Mustafa
  • Shayaan_Mustafa
so i want to say. i have solved this and its proof is too long. approx 3 pages. so..

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anonymous
  • anonymous
i dont think it should be that long though because the other problems only take up like 1/8 of a page
Shayaan_Mustafa
  • Shayaan_Mustafa
yes. but it is.. therefore anyone didn't touch that. i think so.
Shayaan_Mustafa
  • Shayaan_Mustafa
do you have windows 7?
anonymous
  • anonymous
no
Shayaan_Mustafa
  • Shayaan_Mustafa
ok which window?
anonymous
  • anonymous
what?
Shayaan_Mustafa
  • Shayaan_Mustafa
ok wait. i do something.
anonymous
  • anonymous
its ok i can figure it out though.
anonymous
  • anonymous
gracias
Shayaan_Mustafa
  • Shayaan_Mustafa
tan^(2)x-sin^(2)x=(tan^(2)x)(sin^(2)x) Replace tanx with an equivalent expression (sin^(2)x)/(cos^(2)x) using the fundamental identities. (sin^(2)x)/(cos^(2)x)-sin^(2)x To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is cosx^(2). Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions. (sin^(2)x)/(cos^(2)x)-sin^(2)x*(cos^(2)x)/(cos^(2)x) Complete the multiplication to produce a denominator of cosx^(2) in each expression. (sin^(2)x)/(cos^(2)x)-(sin^(2)xcos^(2)x)/(cos^(2)x) Combine the numerators of all expressions that have common denominators. (sin^(2)x-sin^(2)xcos^(2)x)/(cos^(2)x) Factor out the GCF of sinx^(2) from each term in the polynomial. (sin^(2)x(1)+sin^(2)x(-cos^(2)x))/(cos^(2)x) Factor out the GCF of sinx^(2) from sinx^(2)-sinx^(2)cosx^(2). (sin^(2)x(1-cos^(2)x))/(cos^(2)x) Replace 1-cos^(2)x with sin^(2)x using the identity sin^(2)(x)+cos^(2)(x)=1. (sin^(2)x(sin^(2)x))/(cos^(2)x) Multiply sinx^(2) by sinx^(2) in the numerator. (sin^(2)x*sin^(2)x)/(cos^(2)x) Multiply sinx^(2) by sinx^(2) to get sinx^(4). (sin^(4)x)/(cos^(2)x) To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is cosx^(2). Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions. (sin^(2)x)/(cos^(2)x)-sin^(2)x*(cos^(2)x)/(cos^(2)x) Complete the multiplication to produce a denominator of cosx^(2) in each expression. (sin^(2)x)/(cos^(2)x)-(sin^(2)xcos^(2)x)/(cos^(2)x) Combine the numerators of all expressions that have common denominators. (sin^(2)x-sin^(2)xcos^(2)x)/(cos^(2)x) Factor out the GCF of sinx^(2) from each term in the polynomial. (sin^(2)x(1)+sin^(2)x(-cos^(2)x))/(cos^(2)x) Factor out the GCF of sinx^(2) from sinx^(2)-sinx^(2)cosx^(2). (sin^(2)x(1-cos^(2)x))/(cos^(2)x) Replace 1-cos^(2)x with sin^(2)x using the identity sin^(2)(x)+cos^(2)(x)=1. (sin^(2)x(sin^(2)x))/(cos^(2)x) Multiply sinx^(2) by sinx^(2) in the numerator. (sin^(2)x*sin^(2)x)/(cos^(2)x) Multiply sinx^(2) by sinx^(2) to get sinx^(4). (sin^(4)x)/(cos^(2)x) Rewrite the expression using the (sinx)/(cosx)=tanx identity. sin^(2)xtan^(2)x

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