trig problem

brooksy · #1 $Old$ December 9th, 2008, 06:29 AM

hi ive been given this question and im not sure how to do it.

1. a) Prove that cosec^4 x - cot^4 x = cosec^2 x + cot^2 x
b) solve for 90 degrees< x < 180 degrees

cosec^4 x - cot^4 x = 2 - cot x

thanks

jaspreet · #2 $Old$ December 9th, 2008, 06:50 AM

Quote:

Originally Posted by brooksy $View Post$

hi ive been given this question and im not sure how to do it.

1. a) Prove that cosec^4 x - cot^4 x = cosec^2 x + cot^2 x
b) solve for 90 degrees< x < 180 degrees

cosec^4 x - cot^4 x = 2 - cot x

thanks

cosec^4x-cot^4x=(cosec^2x)^2-(cot^2x)^2
=(cosec^2x+cot^2x)(cosec^2x-cot^2x)
=(cosec^2x+cot^2x)
{a^2-b^2=(a-b)(a+b) and cosec^2x-cot^2x=1}

brooksy · #3 $Old$ December 10th, 2008, 01:29 AM

thanks for that. does anyone know how to do part 2. cheers

mathaddict · #4 $Old$ December 10th, 2008, 06:23 AM

Quote:

Originally Posted by brooksy $View Post$

hi ive been given this question and im not sure how to do it.

b) solve for 90 degrees< x < 180 degrees

cosec^4 x - cot^4 x = 2 - cot x

thanks

$cosec^4x-cot^4x=2-cot x$
$cosec^4x-(cosec^4x-1)=2-cot x$
$1=2-cot x$