If `sectheta-costheta=1` ,then `tan^2(theta/2)=`

If : sectheta+costheta=2 "then" : sec^(2)theta-sec^(4)theta=

If sintheta=costheta then 2tan^(2)theta+sin^(2)theta-1=___ .

If costheta_1 =2costheta_2, then tan((theta_1-theta_2)/2)tan((theta_1+theta_2)/2) is equal to

If costheta_1 =2costheta_2, then tan((theta_1-theta_2)/2)tan((theta_1+theta_2)/2) is equal to (a) 1/3 (b) -1/3 (c) 1 (d) -1

If costheta_1 =2costheta_2, then tan((theta_1-theta_2)/2)tan((theta_1+theta_2)/2) is equal to (a) 1/3 (b) -1/3 (c) 1 (d) -1

Prove: (sectheta+costheta)(sectheta-costheta)=tan^2theta+sin^2theta

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

(i) "sin"theta cot theta + "sin"theta cosectheta = 1+ costheta (ii) sectheta(1-"sin"theta) (sectheta+tantheta)=1 (iii) "sin"theta(1+"tan"theta)+costheta(1+cottheta)=sectheta+cosectheta

(i) (sec theta-cos theta)(cosectheta-"sin"theta)=(1)/("tan"theta+cottheta) (ii) ("sin"theta+sectheta)^(2)+(costheta+cosectheta)^(2)=(1+secthetacosectheta)^(2)

For any real theta , (csc theta - sin theta)(sectheta-costheta)(tan theta+cot theta)=......