anonymous
  • anonymous
1 + sec^2 x sin^2 x = sec^2 x Verify this trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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cwrw238
  • cwrw238
LHS: use sec^2 x = 1 /cos^2 x
anonymous
  • anonymous
Thanks for answering but I still don't get it. What do you mean?
cwrw238
  • cwrw238
LHS = 1 + sin^2 x ------- cos^2 x

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cwrw238
  • cwrw238
and sin^2 x ------- = tan^2 x cos^2 x
cwrw238
  • cwrw238
so LHS = 1 + tan^2 x
anonymous
  • anonymous
ok... so let me see if this will help you help me understand this better. I know that I'm supposed to do something with the left side of the equation to make it sec^2x. correct?
cwrw238
  • cwrw238
right
anonymous
  • anonymous
I just don't see how the cos^2x in the denomenator fits in. I'm sorry I truly suck at this :(
cwrw238
  • cwrw238
yes these can be tricky - you must have a good knowledge of the trig identities sometimes you just try different ones to see if there are any connections - i was aiming for 1 + tan^2 x because i knew that sec^2 x = 1 + tan^2 x
cwrw238
  • cwrw238
i introduced the cos^2x because sin^2 x/cos^2 x = tan^2 x and sec^2 x = 1/cos^2 x
anonymous
  • anonymous
OK so how would I put that together to get the answer
cwrw238
  • cwrw238
if you google trigonometrical identities you'll a list of them
anonymous
  • anonymous
starting from the original equation how do I use what you gave me.
cwrw238
  • cwrw238
well we got LHS = 1 + tan^2 x and this equals RHS sec^2 x
anonymous
  • anonymous
yes but then again so does 1+ sec^2x sin^2x. I need to transform (1+sec^2xsin^2x) and make it read sec^2x
cwrw238
  • cwrw238
LHS = 1+sec^2xsin^2x) = 1 + sin^2 x ------ (because sec^2 x = 1 / cos^2 x) cos^2 x = 1 + tan^2x = sec^2 x ( because sec^2x = 1 + tan^2 x is a standard identity) = RHS
anonymous
  • anonymous
Ohhhhh got it wow! OK. Thank you so much. You see I suck so bad that even when you are plainly explaining it to me I still dont get it. But now I do. Again thank you for helping me :)
cwrw238
  • cwrw238
yw
anonymous
  • anonymous
|dw:1354034596449:dw|
anonymous
  • anonymous
above the last equal sign.... what does it say? 1/??
anonymous
  • anonymous
oh wait is it 1/cos^2x ?
anonymous
  • anonymous
yeah sister
anonymous
  • anonymous
awesome.... ok thanks but why is yours different than the other one? is it wrong or is this just another way to do it
cwrw238
  • cwrw238
no - they are both acceptable - just another way to do it

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