Help with a simple trigonometry problem... 10 points

If tan A= 2/3 and cos A < 0, evaluate the expression {[secA(cosA-sinA)]/[tan45+tanAcscA]}+cot squared A

tanA = 2/3 cos A < 0, so A is in 3rd quadrant
sinA = -2/sqrt(13), cosA = -3/sqrt(13)
secA = -sqrt(13)/3
cscA = -sqrt(13)/2
the expression = -sqrt(13)/2*(-3/sqrt(13)+2/sqrt(13))/(1+… + 9/4
= 1/2 / (1-sqrt(13))/3 + 9/4
= 3/(2(1-sqrt(13)) + 9/4

Use the identity 1 + tan² A = sec² A to find sec A
cos A = 1 / sec A
Now use the identity sin² A = cos² A = 1 to find sin A.
We can find cosec A and cot A from the facts that
cosec A = 1 / sin A
cot A = 1 / tan A
Subsitute them all into your expression plus remember that tan 45 = 1