factor and simplify

[baselramjet]

factor and simplify sin^2 x * sec^2 x – sin^2 x

 

[Mrspi]

factor and simplify sin^2 x * sec^2 x – sin^2 x

What have you tried? Could you factor this?

a<SUP>2</SUP> b<SUP>2</SUP> - a<SUP>2</SUP>

Use the same approach on your problem. Then, look at the fundamental identities to see what you might be able to substitute.

Show us your work, and we'll help you see where you went astray.

 

[baselramjet]

this is what I got:

first, factor-

sin^(2)x*sec^(2)x-sin^(2)x

sin^(2)xsec^(2)x-sin^(2)x

sin^(2)x(sec^(2)x)+sin^(2)x(-1)

sin^(2)x(sec^(2)x-1)

sin^(2)x(secx+1)(secx-1)

and then simplify,

sin^(2)x(secx+1)(secx-1)

sin^(2)x(secx*secx+secx*-1+1*secx+1*-1)

sin^(2)x(sec^(2)x-1)

(sin^(2)x(sec^(2)x)+sin^(2)x(-1))

(sin^(2)xsec^(2)x-sin^(2)x)

sin^(2)xsec^(2)x-sin^(2)x

sin^(2)x(sec^(2)x)+sin^(2)x(-1)

sin^(2)x(sec^(2)x-1)

sin^(2)x(tan^(2)x)

sin^(2)x*tan^(2)x

(sin^(2)xtan^(2)x)

sin^(2)xtan^(2)x

(sin^(2)xsin^(2)x)/(cos^(2)x)

(sin^(4)x)/(cos^(2)x)

answer: sin^(2)xtan^(2)x

how is that?

 

[stapel]

answer: sin^(2)xtan^(2)x

how is that?

I can't make heads or tails of what you did. Try following the previous tutor's suggestion, and you should get the book's answer in two steps.

Eliz.

 

[baselramjet]

Factor:

a^(2)b^(2)-a^(2)

a^(2)(b^(2))+a^(2)(-1)

a^(2)(b^(2)-1)

a^(2)(b+1)(b-1)

simplify

a^(2)(b+1)(b-1)

a^(2)(b*b+b*-1+1*b+1*-1)

a^(2)(b^(2)-1)

(a^(2)(b^(2))+a^(2)(-1))

(a^(2)b^(2)-a^(2))

a^(2)b^(2)-a^(2)

 

[stapel]

Factor:

a^(2)b^(2)-a^(2)

a^(2)(b^(2))+a^(2)(-1)

a^(2)(b^(2)-1)

Stop here.

Now do the same thing with your trig expression, and use an identity for the (b² - 1) part.

Eliz.

 

[baselramjet]

Factor:

sin^(2)x*sec^(2)x-sin^(2)x

sin^(2)xsec^(2)x-sin^(2)x

sin^(2)x(sec^(2)x)+sin^(2)x(-1)

sin^(2)x(sec^(2)x-1)

 

[baselramjet]

Simplify:

sin^(2)x(sec^(2)x-1)

sin^(2)x(tan^(2)x)

sin^(2)xtan^(2)x

(sin^(2)xsin^(2)x)/(cos^(2)x)

(sin^(4)x)/(cos^(2)x)

sin^(2)xtan^(2)x

 

[stapel]

Simplify:

sin^(2)x(sec^(2)x-1)

sin^(2)x(tan^(2)x)

sin^(2)xtan^(2)x

You were done at this point. The following three lines were unnecessary.

Eliz.