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mica

  • 3 years ago

need help im stuck i need to prove that (1-tan x)(1+tan x) = (1-2sin^2x)(sec^2x)

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  1. mica
    • 3 years ago
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    i forgot to mention that i have to start on the left side x.x

  2. mica
    • 3 years ago
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    i original problem is prove: cos2x = 1 - tan^2x ---------- 1+tan^2x

  3. jiteshmeghwal9
    • 3 years ago
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    \[(1-\frac{sinx}{cosx}){(1+\frac{sinx}{cosx})}\]\[(1-\frac{\sin^2x}{\cos^2x})\]\[1-\sin^2x \times \frac{1}{\cos^2x}\]\[(1-\sin^2x)(\sec^2x).\]

  4. mica
    • 3 years ago
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    aaaaaaaaaa lol gotcha xD thank you

  5. jiteshmeghwal9
    • 3 years ago
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    yw :)

  6. myininaya
    • 3 years ago
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    ?

  7. myininaya
    • 3 years ago
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    \[(1+\tan(x))(1-\tan(x))\] \[1-\tan^2(x)\] \[1-\frac{\sin^2(x)}{\cos^2(x)}\] He is right until this point.

  8. jiteshmeghwal9
    • 3 years ago
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    ? ------> ??

  9. jonny1
    • 3 years ago
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    hi

  10. myininaya
    • 3 years ago
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    Hint 1: Combine the fractions

  11. myininaya
    • 3 years ago
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    Hint 2: Rewrite the numerator in terms of sin by using the Pythagorean identity, \[\cos^2(x)=1-\sin^2(x)\]

  12. jiteshmeghwal9
    • 3 years ago
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    |dw:1352617552352:dw|

  13. myininaya
    • 3 years ago
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    Yes but that totally is not the same as (1-sin^2(x))(sec^2(x))

  14. jiteshmeghwal9
    • 3 years ago
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    well, i can be wrong here because i'm only studying in middle school

  15. myininaya
    • 3 years ago
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    Recall the distributive property a(b+c)=ab+ac

  16. myininaya
    • 3 years ago
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    1 is not being multiplied by sec^2(x) so you can not write (1-sin^2(x))(sec^2(x))

  17. myininaya
    • 3 years ago
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    @mica you leave already?

  18. myininaya
    • 3 years ago
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    Try not to give the full solution next time either even though you didn't do it this time because did it incorrectly anyways.

  19. jiteshmeghwal9
    • 3 years ago
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    He isn't worrying about his question :)

  20. jiteshmeghwal9
    • 3 years ago
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    Okay mam sorry. Thanx for the advice :)

  21. myininaya
    • 3 years ago
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    Scenario 1: He just copied what you had and left because he got what he thought he wanted. Scenario 2: He had chores.

  22. myininaya
    • 3 years ago
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    We don't want Scenario 1. We want people to actually learn.

  23. jiteshmeghwal9
    • 3 years ago
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    okay mam :)

  24. 03225186213
    • 3 years ago
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    (cos^x−sin^2x)(sec^2x) cos^x=1-sin^2x plug and get ans.

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