My Math Forum Proving Trigonometric Identities

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 June 11th, 2010, 08:01 PM #1 Newbie   Joined: Jun 2010 Posts: 5 Thanks: 0 Proving Trigonometric Identities Hi everyone. Just wondering if anyone can solve these trigonometric questions. Q1: (cos^2 theta)/(1 + sin theta)= 1 - sin theta Q2: cosec^2 theta + sec^2 theta=(tan theta + cos^2 theta) Thanks
 June 11th, 2010, 08:48 PM #2 Member   Joined: Jun 2010 Posts: 35 Thanks: 0 Re: Proving Trigonometric Identities 1) In the norminator there is $cos^2Theta=1-sin^2Theta$ $1-sin^2Theta=(1+sinTheta)(1-sinTheta)$ $\frac {(1-sintheta)(1+sinTheta)}{1+sinTheta}$ and $1+sinTheta$ cancel so there is the first identity.
 June 12th, 2010, 06:25 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 Q1: As above, cos²?/(1 + sin ?) = 1 - sin(?), but only when sin ? ? -1. Q2: Not an identity.
June 12th, 2010, 06:38 AM   #4
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Re: Proving Trigonometric Identities

Hello, muito_bossa!

You said "solve these questions" . . . ??

[color=beige]. . [/color]We solve equations.

Did you mean "Prove the identities" ?

Quote:
 $[1]\;\;\frac{\cos^2\theta}{1\,+\,\sin\theta} \:=\: 1\,-\,\sin\theta$

$\text{The left side is: }\;\frac{\cos^2\theta}{1\,+\,\sin\theta} \;=\;\frac{1\,-\,\sin^2\theta}{1\,+\,\sin\theta} \;=\;\frac{(1\,-\,\sin\theta)(1\,+\,\sin\theta)}{1\,+\,\sin\theta} \;=\;1\,-\,\sin\theta$

Quote:
 $[2]\;\;\csc^2\theta\,+\,\sec^2\theta \:=\:\tan\theta \,+\, \cos^2\theta$

This is not an identity . . .

 June 12th, 2010, 03:16 PM #5 Newbie   Joined: Jun 2010 Posts: 5 Thanks: 0 Re: Proving Trigonometric Identities Thanks for the help. In regards to Q2 I think that it might be an error from the textbook as I've pretty much tried everything but to no avail.

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