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## koli123able 2 years ago Prove: cotx+tanx=cotx * sec^2x

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1. hartnn

write sec^2x = .... ?

2. koli123able

1/cos^2x

3. hartnn

1+ tan^2 x ?

4. koli123able

sec^2x

5. hartnn

then you can use directly here, tan x cot x =1

6. klimenkov

All you need to know is the definition of \(\tan x, \cot x, \sec x\) and how to work with fractions.

7. hartnn

yes, so i said to replace sec^2 x by 1+tan^2x

8. hartnn

can be solved without involving fractions ... :)

9. hartnn

@koli123able did you try ?

10. koli123able

which side to choose?

11. hartnn

right ...?

12. hartnn

cotx * sec^2x=cotx * (1+tan^2 x) =..... ?

13. koli123able

cotx+ cotx tan^2x

14. KAOS|abdullah

cotx tanx becomes 1

15. hartnn

cotx+ cotx tan^2x = cot x + tan x (cot x tan x)

16. koli123able

is that an identity cot x tanx =1 ??

17. hartnn

absolutely. tan x = 1/cot x so, tan x cot x =1

18. noureddine92

cosx/sinx =sinx/cosx

19. noureddine92

cos^2x + sin^2x / cosx sinx

20. noureddine92

1/cosxsinx

21. noureddine92

cscx+secx

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