Prove the following Identity: `(tan alpha+sec alpha-1)/(tan alpha-sec alpha+1)=(1+sin alpha)/(cos alpha)`

Prove the following identities: (sin alpha sin 11 alpha + sin 3 alpha sin 7 alpha)/(sin alpha cos 11 alpha + sin 3 alpha cos 7 alpha)= tan 8 alpha

tan2alpha-tanalpha(1+sec2alpha)=

Prove the following identities: (1-sin alpha+cosalpha)^2=2(1+cos alpha)(1-sin alpha)

(sec8 alpha-1)/(sec4 alpha-1)=(tan8 alpha)/(tan2 alpha)

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

tan theta = (sin alpha-cos alpha) / (sin alpha + cos alpha)

Prove that, (sec 8 alpha -1)/(sec 4 alpha-1)= (tan 8 alpha)/(tan 2 alpha

Prove that, (sin alpha + cos alpha)/(cos alpha-sin alpha)=tan2 alpha + sec 2 alpha

(1)/(sec alpha - tan alpha ) - (1)/( cos alpha)=

Find the adjoint of the following matrices: [1tan alpha sin alpha sin alpha cos alpha]( ii) [1tan alpha/2-tan alpha/21] Verify that (adjA)A=|A|I=A(adjA) for the above matrices.