1. ## trig problem

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

2. Originally Posted by brooksy
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}

3. ## thanks

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

4. Originally Posted by brooksy
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

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

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### prove that cosec4a cosec8a=cot2a-cot8a ?.com

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