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I can't figure out this trig problem?
I need to simplify the expression 1+tanx/sinx - secx down to cscx.
Help?
3 Answers
- lukeLv 49 years agoFavorite Answer
(1+tanx)/sinx - secx
=(1+(sinx/cosx))/sinx - secx
=(1/sinx)+(sinx/cosx/sinx) - secx
=(1/sinx)+(1/cosx)-(1/cosx)
=1/sinx
=cscx
- KateLv 59 years ago
1 + tanx / sinx - secx
1 + (sinx/cosx * 1/sinx) - secx
1 + 1/cosx - secx
1
Sorry, I'm not getting that.
- ?Lv 49 years ago
tan(x) = sin(x)/cos(x)
sec(x) = 1/cos(x)
csc(x) = 1/sin(x)
(1+tanx)/sinx - secx = [1 + sin(x)/cos(x)]/sin(x) - 1/cos(x) =
= {[cos(x) + sin(x)]/[cos(x)]}/{sin(x)} - 1/cos(x) =
= [cos(x) + sin(x)]/[cos(x)*sin(x)] - 1/cos(x) =
= 1/sin(x) + 1/cos(x) - 1/cos(x) = 1/sin(x) = 1/csc(x)
So there you go, but I wish you had written (1+tanx)/sinx instead of 1+tanx/sinx because it looks like sinx is only dividing tanx instead of 1 + tanx.
I hope this helps...
