Lindsey11x16
  • Lindsey11x16
cos^x(sec^2x-1) what pythagoream identiy to use?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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hartnn
  • hartnn
first multiply them out. like a(b-c) = ab-ac so whats cos^x(sec^2x-1) = ... - ... ?
anonymous
  • anonymous
yeahhhhh right hartnn
Lindsey11x16
  • Lindsey11x16
cos^2x(sec^2x) - cos^2x-1

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hartnn
  • hartnn
yup, and you know what cos x * sec x = .. ?
hartnn
  • hartnn
and -1 won't come.
hartnn
  • hartnn
\(\large \cos^2x(\sec^2x-1)=\cos^2x\sec^2x-\cos^2x = ...?\)
hartnn
  • hartnn
can u simplify that ^ ? use the fact that cos x = 1/ sec x.
Lindsey11x16
  • Lindsey11x16
should i use factorization in this
hartnn
  • hartnn
nopes. since, cos x = 1/ sec x what is cos x * sec x = ... ?
Lindsey11x16
  • Lindsey11x16
should i turn secant into cos
hartnn
  • hartnn
yes., do that...what u get ?
Lindsey11x16
  • Lindsey11x16
|dw:1355024922967:dw|
hartnn
  • hartnn
1 is correct.
hartnn
  • hartnn
\(\large \cos^2x\sec^2x-\cos^2x = 1- \cos^2 x=...?\)
Lindsey11x16
  • Lindsey11x16
equals sinx^2
Lindsey11x16
  • Lindsey11x16
?
hartnn
  • hartnn
use th identity \(\huge \color{red}{\sin^2x+\cos^2x=1}\) yes, sin^2 x is correct :)
Lindsey11x16
  • Lindsey11x16
thanks! this is hard cuz cuz i never know which identity to use :(
hartnn
  • hartnn
do u wanna know alternative way to solve this ? using other identity...
Lindsey11x16
  • Lindsey11x16
yep
hartnn
  • hartnn
using \(\huge \color{red}{\sec^2x=1+\tan^2x}\) what can you write (sec^2x-1)=...?
Lindsey11x16
  • Lindsey11x16
sec^2x-1 = tan
hartnn
  • hartnn
its \(\tan^2x\)
hartnn
  • hartnn
and you can write tan^2 x as sin^2 x/ cos^2x
hartnn
  • hartnn
so, put (sec^2 x-1) as sin^2 x/ cos^2x cos^2 x*( sin^2 x/ cos^2x) will again give you sin^2 x
Lindsey11x16
  • Lindsey11x16
|dw:1355025560186:dw|
hartnn
  • hartnn
yup.
Lindsey11x16
  • Lindsey11x16
thank you ! <3
hartnn
  • hartnn
welcome ^_^

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