if `costheta-sintheta=1` then `theta`

If (costheta+sintheta)/(costheta-sintheta)=8 then the value of cot theta is equal to:

Prove that: (i) (costheta)/(1-sintheta)=(1+sintheta)/(costheta) (ii) (1+costheta-sin^(2)theta)/(sintheta+sinthetacostheta)=cottheta (iii) 1+(tan^(2)theta)/(1+sectheta)=sectheta

The locus of the point (a(costheta+sintheta),b(costheta-sintheta)) , where theta is the parameter, is

Eliminate theta and phi costheta +sintheta=a , sintheta*costheta =b

(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta

(sintheta)/(1+costheta) + (1+costheta)/(sintheta) = 2 cosec theta

sintheta/(1-cottheta)+costheta/(1-tantheta)= (a) theta (b)1 (c) costheta-sintheta (d) costheta+sintheta

Simplify costheta[[costheta, sin theta],[-sintheta, costheta]]+sintheta[[sintheta, -costheta],[costheta, sintheta]]

If sintheta + cos theta =1 , then the value of sintheta - costheta is:

Prove that (1+costheta+sintheta)/(1-costheta+sintheta)=cot(theta/2)