## Lindsey11x16 2 years ago cos^x(sec^2x-1) what pythagoream identiy to use?

1. hartnn

first multiply them out. like a(b-c) = ab-ac so whats cos^x(sec^2x-1) = ... - ... ?

2. jishan

yeahhhhh right hartnn

3. Lindsey11x16

cos^2x(sec^2x) - cos^2x-1

4. hartnn

yup, and you know what cos x * sec x = .. ?

5. hartnn

and -1 won't come.

6. hartnn

$$\large \cos^2x(\sec^2x-1)=\cos^2x\sec^2x-\cos^2x = ...?$$

7. hartnn

can u simplify that ^ ? use the fact that cos x = 1/ sec x.

8. Lindsey11x16

should i use factorization in this

9. hartnn

nopes. since, cos x = 1/ sec x what is cos x * sec x = ... ?

10. Lindsey11x16

should i turn secant into cos

11. hartnn

yes., do that...what u get ?

12. Lindsey11x16

|dw:1355024922967:dw|

13. hartnn

1 is correct.

14. hartnn

$$\large \cos^2x\sec^2x-\cos^2x = 1- \cos^2 x=...?$$

15. Lindsey11x16

equals sinx^2

16. Lindsey11x16

?

17. hartnn

use th identity $$\huge \color{red}{\sin^2x+\cos^2x=1}$$ yes, sin^2 x is correct :)

18. Lindsey11x16

thanks! this is hard cuz cuz i never know which identity to use :(

19. hartnn

do u wanna know alternative way to solve this ? using other identity...

20. Lindsey11x16

yep

21. hartnn

using $$\huge \color{red}{\sec^2x=1+\tan^2x}$$ what can you write (sec^2x-1)=...?

22. Lindsey11x16

sec^2x-1 = tan

23. hartnn

its $$\tan^2x$$

24. hartnn

and you can write tan^2 x as sin^2 x/ cos^2x

25. hartnn

so, put (sec^2 x-1) as sin^2 x/ cos^2x cos^2 x*( sin^2 x/ cos^2x) will again give you sin^2 x

26. Lindsey11x16

|dw:1355025560186:dw|

27. hartnn

yup.

28. Lindsey11x16

thank you ! <3

29. hartnn

welcome ^_^