Help with proving trig identities

[ninatemple]

1. 1/sin x - sin x = cos x/tan x

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2. 1/cos + tan x = cos x/1-sin x

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3. tan x sin x/ 1-cos x = 1 + 1/cos x

 

[Deleted member 4993]

1. 1/cos x + tan x = cos x/[1-sinx] ... use those [] to indicate order of operations .... very very important!!

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2. tan x sin x/[1-cos x] = 1 + 1/cos x

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3. 1/sin x - sin x = cos x/tan x ...... see http://www.freemathhelp.com/forum/threads/91857-Need-Help-With-Proving-Trig-Identities

1/cos x + tan x = cos x/[1-sinx]

L.H.S. =

1/cos(x) + tan(x)

= 1/cos(x) + sin(x)/cos(x)

= [1 + sin(x)]/cos(x)

= [1 + sin(x)]/cos(x) * [1 - sin(x)]/[1 - sin(x)]

= [1 - sin²(x)]/{cos(x)*[1 - sin(x)]} .... continue....


2. tan x sin x/[1-cos x] = 1 + 1/cos x

L.H.S.

= tan x * sin x/[1-cos x]

= tan x * sin x/[1-cos x] * [1+ cos x]/[1+ cos x]

= tan x * sin x * [1+ cos x]/[1- cos²x] ....... continue......