Remember odd and even functions?
Sec(-x)=Sec(x) because Sec is even
Sin(-x)=-Sin(x) because Sin is odd
Tan(-x)=-Tan(x) because Tan is odd
(1 + sec (-x))/ (sin(-x) + tan(-x))
So we rewrite the left side as
(1+sec(x))/(-sin(x)-tan(x))
From here you have a couple options, I think, but I would convert everything to sin and cos.
(1+(1/cos(x))/(-sin(x)-(sin(x)/cos(x)))
Now, find the LCD's
((cos(x)+1)/cos(x))/((-sin(x)cos(x)-sin(x))/cos(x)
Now, remember that dividing is the same as multiplying by the reciprocal.
[cos(x)+1]/cos(x) X cos(x)/[-sin(x)cos(x)-sin(x)]
Cosines cancel, so we get:
[cos(x)+1]/[-sin(x)cos(x)-sin(x)]
Now we factor out the -sin(x) in the denominator.
[cos(x)+1]/[-sin(x)(cos(x)+1)]
Now it's simple: cos(x)+1 in the numerator and denominator, so they cancel, and we get:
1/-sin(x)=-csc(x)
Try doing the second problem on your own using these techniques.
