If n is an integer , prove that , `tan(npi+alpha)=tan alpha`

If n is an integer, prove that, (iv) tan (n pi + alpha) = tan alpha

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha

If alpha + beta + gamma + delta = 2pi then prove that sum tan alpha = tan alpha *tan beta* tan gamma* tan delta *sum cot alpha .

Prove that cot alpha - tan alpha =2 cot 2 alpha.

If sin theta=n sin(theta+2 alpha), prove that tan(theta+alpha)=(1+n)/(1-n)tan alpha

If 0 lt alpha lt beta lt (pi)/(2) , prove that, tan alpha-tan beta lt alpha-beta .

If tanbeta =(sin alpha cos alpha)/(2 + cos^(2) alpha),"prove that " 3 tan (alpha -beta).=2 tan alpha

If sin (theta + alpha ) = cos ( theta + alpha), prove that tan theta =(1- tan alpha )/(1 + tan alpha )