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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

i forgot to mention that i have to start on the left side x.x

2. mica

i original problem is prove: cos2x = 1 - tan^2x ---------- 1+tan^2x

3. 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).$

4. mica

aaaaaaaaaa lol gotcha xD thank you

5. jiteshmeghwal9

yw :)

6. myininaya

?

7. 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.

8. jiteshmeghwal9

? ------> ??

9. jonny1

hi

10. myininaya

Hint 1: Combine the fractions

11. myininaya

Hint 2: Rewrite the numerator in terms of sin by using the Pythagorean identity, $\cos^2(x)=1-\sin^2(x)$

12. jiteshmeghwal9

|dw:1352617552352:dw|

13. myininaya

Yes but that totally is not the same as (1-sin^2(x))(sec^2(x))

14. jiteshmeghwal9

well, i can be wrong here because i'm only studying in middle school

15. myininaya

Recall the distributive property a(b+c)=ab+ac

16. myininaya

1 is not being multiplied by sec^2(x) so you can not write (1-sin^2(x))(sec^2(x))

17. myininaya

@mica you leave already?

18. 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.

19. jiteshmeghwal9

He isn't worrying about his question :)

20. jiteshmeghwal9

Okay mam sorry. Thanx for the advice :)

21. myininaya

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

We don't want Scenario 1. We want people to actually learn.

23. jiteshmeghwal9

okay mam :)

24. 03225186213

(cos^x−sin^2x)(sec^2x) cos^x=1-sin^2x plug and get ans.

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