if p = secA - tanA and q = cosecA + cotA. Then what is q in terms of p.

Question

I have been given four options.

1) p+1/p-1

2)1+p/1-p

3)p-1/p+1

4)1-p/1+p

I would appreciate the help.

Answer 1

I got (1 + p)/(1 - p) which is essentially option 2) .

There is a lot of algebra involved.

The strategy is to work a bit with the given functions to arrive at

cos(A) = (q - 1)/(q p +1) and sin(A) = (p + 1) /( q p +1 ) and

A = arctan( ( p +1) /(q -1) )

The standard triangle construction then gives

sin(A) = (p+1) / SS and cos(A) = (q - 1)/SS where SS = sqrt( (p+1)^2 +(q-1)^2)

It is easy to show that q = (1 + cos(A) )/(sin( A))

From there make the substitutions for sin(A) and cos(A) and a lot of algebra.