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If tan ^(2) theta=1-k^(2), show that sec...

If `tan ^(2) theta=1-k^(2)`, show that `sec theta+tan ^(3) theta cosectheta=(2-k^(2))^(3 / 2)`

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sec theta+tan ^(3) theta (cosec) theta=(1)/(cos theta)+(tan ^(2) theta)/(cos theta)=(1+tan ^(-) theta)/(cos theta)=(1+tan ^(2) theta) sec theta.
.=(1+tan ^(2) theta) sqrt(1+tan ^(2) theta)=(1+tan ^(2) theta)^(3 / 2)=(1+1-k^(2))^(3 / 2) .(2-k^(2))^(3 n).
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