Question

Does anyone can help me to prove that ...

Answer 1

hello : 
by identity : cos²(x)+sin²(x) = 1
divide by cos²(x) :
cos²(x) /cos²(x) +sin²(x)cos²(x)/ = 1/cos²(x)
1+sin²(x)cos²(x)/ = 1/cos²(x)
1+ (sin(x)/cos(x))² = 1/cos²(x)
1+tan²(x) =  1/cos²(x)
conclusion : 
tan²(x) =  1/cos²(x) -1