## mica Group Title need help im stuck i need to prove that (1-tan x)(1+tan x) = (1-2sin^2x)(sec^2x) one year ago one year ago

1. mica Group Title

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

2. mica Group Title

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

3. jiteshmeghwal9 Group Title

$(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 Group Title

aaaaaaaaaa lol gotcha xD thank you

5. jiteshmeghwal9 Group Title

yw :)

6. myininaya Group Title

?

7. myininaya Group Title

$(1+\tan(x))(1-\tan(x))$ $1-\tan^2(x)$ $1-\frac{\sin^2(x)}{\cos^2(x)}$ He is right until this point.

8. jiteshmeghwal9 Group Title

? ------> ??

9. jonny1 Group Title

hi

10. myininaya Group Title

Hint 1: Combine the fractions

11. myininaya Group Title

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

12. jiteshmeghwal9 Group Title

|dw:1352617552352:dw|

13. myininaya Group Title

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

14. jiteshmeghwal9 Group Title

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

15. myininaya Group Title

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

16. myininaya Group Title

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

17. myininaya Group Title

18. myininaya Group Title

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 Group Title

He isn't worrying about his question :)

20. jiteshmeghwal9 Group Title

Okay mam sorry. Thanx for the advice :)

21. myininaya Group Title

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 Group Title

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

23. jiteshmeghwal9 Group Title

okay mam :)

24. 03225186213 Group Title

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