Prove that `(1-sintheta+costheta)/(sintheta+costheta-1)=(1+costheta)/sintheta`

Prove that : (sintheta-costheta)/(sintheta+costheta)+(sintheta+costheta)/(sintheta-costheta)=(2)/(2sin^(2)theta-1)

prove that- (sintheta+1-costheta)/(costheta-1+sintheta)=(1+sintheta)/costheta

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

If (1+ sintheta-costheta)/(1+ sintheta + costheta)+(1+sintheta+costheta)/(1+sintheta-costheta)= 4 , then which of the following values will be suitable for theta ?

The value of (sintheta+costheta-1)/(sintheta-costheta+1)xxsqrt((1+sintheta)/(1-sintheta)) is:

(costheta*csctheta-sintheta*sectheta)/(costheta+sintheta)

Prove that : (1+sintheta)/(costheta)+(costheta)/(1+sintheta)=2sectheta

Prove that : (1-costheta)/(sintheta)+(sintheta)/(1-costheta)=2"cosec "theta

costheta[(costheta, sintheta),(-sintheta,costheta)]+sintheta[(sintheta,-costheta),(costheta,sintheta)] is equal to (A) [(0,0),(1,1)] (B) [(1,1),(0,0)] (C) [(0,1),(1,0)] (D) [(1,0),(0,1)]