" 13.If "tan^(2)x=1-b^(2)" ,show that "sec x+tan^(3)x cosec x=+-(2-k^(2))^(3/2)

If tan^(2)theta = 1 - k^(2) , show that sec theta + tan^(3)theta cosec theta = (2 - k^(2))^(3//2) . Also, find the values of k for which this result holds.

If tan^(2)theta = (1-e^2) show that sec theta + tan^(3). "cosec" theta = (2-e^(2))^(3//2) .

tan^(2)x = 3"cosec"^(2)x-1

If tan theta=k , then show that sec theta+tan^(3)theta "cosec"theta=(1+k^(2))^((3)/(2)) .

2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

Prove that :sec^(6)x-tan^(6)x-3sec^(2)x" ."tan^(2)x=1

Show that 2 tan^-1 x = cosec^-1((1+x^2)/(2x)), 0 < |x| le 1

Show that tan 3 x=(3 tan x-tan ^(3) x)/(1-3 tan ^(2) x)