Verify the identity 1 sec2 x sin2 x sec2 xSolution6 1sec2x

Verify the identity. 1 + sec^2 x sin^2 x = sec^2 x

Solution

6) 1+sec²xsin²x

write secx as 1/cosx

=1+ (1/cos²x)sin²x

=(cos²x+sin²x)/cos²x

=1/cos²x , since cos²x+sin²x =1 is an identity

=(1/cosx)²

write 1/cosx as secx

=(sec²x)