Prove the following identity: `(1+t a nalphat a nbeta)^2+(tanalpha-t a nbeta)^2=sec^2alphasec^2beta`

Prove the following identity: (1+tan alpha tan beta)^(2)+(tan alpha)(tan alpha-tan beta)^(2)=sec^(2)alpha sec^(2)beta

What is (1+tanalphatanbeta)^(2)+(tanalpha-tanbeta)^(2)-sec^(2)alphasec^(2)beta equal to

Prove the following identities: (cos alpha cos beta+sin alphasin beta)^2+(sinalphacos beta-cos alphasinbeta)^2=1

Prove the following identities: sinalpha cosalpha(tanalpha-cotalpha)=2sin^2alpha-1

Prove the following identity: (1+cottheta-cos e ctheta)(1+t a ntheta+s e ctheta)=2

tan2alpha-tanalpha(1+sec2alpha)=

Prove the following identities: sec(alpha + beta) = (sec alpha sec beta)/(1 - tan alpha tan beta)

Prove the following identity: costheta(t a ntheta+2)(2t a ntheta+1)=2s e ctheta+5sintheta

Prove the following identity : (sin theta+ sec theta)^2 +(cos theta+ cosec theta)^2= (1+ sec theta cosec theta)^2 .

Prove the following identity : (1 - tan x)^2+(1 -cot x)^2 = (sec x -cosec x)^2 .