Question

PLEASE PLEASE PLEASE HELP ASAP

Answer 1

Explanation:

We can start by simplifying the denominator, which is cot(a) + tan(a):

cot(a) + tan(a) = cos(a)/sin(a) + sin(a)/cos(a)

To combine these terms, we can find a common denominator of sin(a)cos(a):

cos^2(a)/(sin(a)cos(a)) + sin^2(a)/(sin(a)cos(a))

= (cos^2(a) + sin^2(a))/(sin(a)cos(a))

= 1/(sin(a)cos(a))

Now we can substitute this expression into the original equation:

sec(a)/(cot(a) + tan(a))

= sec(a) / (1/(sin(a)cos(a)))

= sec(a) * (sin(a)cos(a))

= (1/cos(a)) * (sin(a)/cos(a))

= sin(a)/cos^2(a)

= csc(a)sec(a)

Therefore, the simplified form of sec(a)/(cot(a) + tan(a)) is csc(a)sec(a).