kaisan 2 years ago simplify the expression: (sinx-1)(tanx+secx) help pretty please

1. kaisan

?

2. kaisan

should i convert the tan and sec to sin and cos?

3. jaersyn

yes

4. Argonx16

Always start by breaking up Tangent/Cosecant/Secant/Cotangent into their constituents.

5. lgbasallote

ahh..an interesting question >:))

6. bmp

That simplifies to -cosx, right? If someone could check :-).

7. kaisan

i'm confused on what to do next >.<' i got this: |dw:1334814256375:dw|

8. Argonx16

You're pretty close. Remember that Secant is 1/Cosine, not 1/Sine.

9. jaersyn

that would make the problem infinitely easier haha

10. kaisan

|dw:1334814461856:dw| so then so i just put them together?

11. Argonx16

Given $(sin(x-1))(tanx+secx)$ Simplify RHS $(\sin(x-1)) * ((sinx/cosx)+(1/cosx))$ Which if you add the RHS together you should get $(\sin(x-1))(1+sinx/cosx)$ And then you multiply.

12. kaisan

i multiply straight across?

13. lgbasallote

i think it was just $\large sinx - 1$right?

14. kaisan

the first part is

15. lgbasallote

so it'll be $\large \mathbf{(sinx-1)*\frac{sinx+1}{cosx}}$ $\large \mathbf{\frac{(sinx-1)(sinx + 1)}{cosx}}$

16. lgbasallote

i'll let you guys do the rest :P Hint: difference of two squares

17. Argonx16

Oooh. I see what I did. That makes sense :D

18. kaisan

i got it ty ^^

19. kaisan

no wait its supposed to be negative but i got positive