mica
  • mica
need help im stuck i need to prove that (1-tan x)(1+tan x) = (1-2sin^2x)(sec^2x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mica
  • mica
i forgot to mention that i have to start on the left side x.x
mica
  • mica
i original problem is prove: cos2x = 1 - tan^2x ---------- 1+tan^2x
jiteshmeghwal9
  • jiteshmeghwal9
\[(1-\frac{sinx}{cosx}){(1+\frac{sinx}{cosx})}\]\[(1-\frac{\sin^2x}{\cos^2x})\]\[1-\sin^2x \times \frac{1}{\cos^2x}\]\[(1-\sin^2x)(\sec^2x).\]

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mica
  • mica
aaaaaaaaaa lol gotcha xD thank you
jiteshmeghwal9
  • jiteshmeghwal9
yw :)
myininaya
  • myininaya
?
myininaya
  • myininaya
\[(1+\tan(x))(1-\tan(x))\] \[1-\tan^2(x)\] \[1-\frac{\sin^2(x)}{\cos^2(x)}\] He is right until this point.
jiteshmeghwal9
  • jiteshmeghwal9
? ------> ??
anonymous
  • anonymous
hi
myininaya
  • myininaya
Hint 1: Combine the fractions
myininaya
  • myininaya
Hint 2: Rewrite the numerator in terms of sin by using the Pythagorean identity, \[\cos^2(x)=1-\sin^2(x)\]
jiteshmeghwal9
  • jiteshmeghwal9
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myininaya
  • myininaya
Yes but that totally is not the same as (1-sin^2(x))(sec^2(x))
jiteshmeghwal9
  • jiteshmeghwal9
well, i can be wrong here because i'm only studying in middle school
myininaya
  • myininaya
Recall the distributive property a(b+c)=ab+ac
myininaya
  • myininaya
1 is not being multiplied by sec^2(x) so you can not write (1-sin^2(x))(sec^2(x))
myininaya
  • myininaya
@mica you leave already?
myininaya
  • myininaya
Try not to give the full solution next time either even though you didn't do it this time because did it incorrectly anyways.
jiteshmeghwal9
  • jiteshmeghwal9
He isn't worrying about his question :)
jiteshmeghwal9
  • jiteshmeghwal9
Okay mam sorry. Thanx for the advice :)
myininaya
  • myininaya
Scenario 1: He just copied what you had and left because he got what he thought he wanted. Scenario 2: He had chores.
myininaya
  • myininaya
We don't want Scenario 1. We want people to actually learn.
jiteshmeghwal9
  • jiteshmeghwal9
okay mam :)
anonymous
  • anonymous
(cos^x−sin^2x)(sec^2x) cos^x=1-sin^2x plug and get ans.

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