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

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

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

Prove that, tan 8alpha - tan 5 alpha - tan 3 alpha = tan 8alpha tan 5 alpha tan 3 alpha

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

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))

If sec alpha=(5)/(4), evaluate (1-tan alpha)/(1+tan alpha)

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

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

If alpha_(1),alpha_(2),alpha_(3),...,alpha_(n) are in A.P whose common common difference is d then sin d[sec alpha_(1)sec alpha_(2)+sec alpha_(2)sec alpha_(3)+...+sec alpha_(n-1)sec alpha_(n)]=tan alpha_(n)-tan alpha_(1)