[" 12.If "phi(x)=(1-x)/(1+x)" ,prove that "],[qquad [" (i) "phi{phi(x)}=x," (ii) "phi{phi(cot theta)}=cot theta]]

If phi(x)=(1-x)/(1+x) prove that phi{phi(x)}=x

If phi(x)=(1-x)/(1+x) prove that phi{phi(cottheta)}=cottheta

If phi(x)=(1-x)/(1+x) , show that, phi(cos2 theta)=tan ^2theta.

If phi(x)=2^(mx+1) , show that phi(a). phi(b).phi(c)=4.phi(a+b+c).

Prove that, "cosec" (theta + phi)=("cosec" theta "cosec" phi)/(cot theta + cot phi)

Prove that (tan phi)/(1-cot phi)+(cot phi)/(1-tan phi)=1+tan phi+cot phi

Prove that sin^(2)phi(1+cot^(2)phi)=1

(sin ( theta -phi))/(sin theta sin phi) = cot phi - cot theta.

If phi(x)=phi'(x) and phi(1)=2, then phi(3) equals

If theta and phi lie in the first quadrant such that sin theta =(8)/(17) "and cos " phi =(12)/(13) find the values of (i) " sin"(theta- phi) " "(ii) " cos " (theta + phi) " " (iii) " tan " (theta - phi)