show that

Neha · 2006-11-30 12:54:41

csc^2 x - cot^2 x
--------------------- = cos^2 x
1 + tan^2 x

1 cos^2x
----- - ---------
sin^2x sin^2x
----------------------- = cos^2x
cos^2x sin^2x
-------- + --------
cos^2x cos^2x

but 1 - cos^2 x = sin^2x, and Sin^2x + cos^2x = 1, so the whole thing boils down to

1
--------------- = cos^2x
1
--------
cos^2 x

Neha · 2006-11-30 12:56:00

rules are

cos x = 1 / sec x sec x = 1 / cos x
sin x = 1 / csc x csc x = 1 / sin x
tan x = sin x / cos x cot x = cos x / sin x

--------------------------------------------------
cos^2 (x) + sin^2 (x) = 1

1 + cot^2 x = csc^2 x

Neha · 2006-11-30 12:59:44

i need help on this one:

now i need help on this one......

sec^2(theta) tan(theta) - tan^3(theta)
---------------------------------------------- - cos^2(theta) = sin^2(theta)
tan(theta)

now i did only up to here :

1 ^2 sin x sin x ^3
--- * ----- - -----
cosx cos x cos x 1 ^2
--------------------------------------- - ---- = sin^3(theta)
sin x sec
------
cos x

Zhylliolom · 2006-11-30 13:26:08

There's another "rule" that you don't have up there that helps solve this one: sec² θ - tan² θ = 1. Watch how it solves the problem:

Zhylliolom · 2006-11-30 13:29:05

And also a word of advice: It looks like in your attempt at the identity I solved for you that you were working with both sides of the equation (multiplying each side by sin θ, for example). Usually, you're best off to stick with one side of the identity (in most cases the uglier looking side) and try to make it look like the other side.

Neha · 2006-12-01 01:48:30

oh i see thanks for the help and advice.
but if i did do it the way i did the other question it would come out to the same answer?

Math Is Fun Forum

#1 2006-11-30 12:54:41

show that

#2 2006-11-30 12:56:00

Re: show that

#3 2006-11-30 12:59:44

Re: show that

#4 2006-11-30 13:26:08

Re: show that

#5 2006-11-30 13:29:05

Re: show that

#6 2006-12-01 01:48:30

Re: show that

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