cos^x(sec^2x-1) what pythagoream identiy to use?

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cos^x(sec^2x-1) what pythagoream identiy to use?

Mathematics
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first multiply them out. like a(b-c) = ab-ac so whats cos^x(sec^2x-1) = ... - ... ?
yeahhhhh right hartnn
cos^2x(sec^2x) - cos^2x-1

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

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