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If tan^2 theta= 1-e^2 prove that sec th...

If `tan^2 theta= 1-e^2` prove that `sec theta + tan^3 theta cosec theta`= `(2-e^2)^(3/2)`

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Given:` tan^2 theta = 1- e^2`
L.H.S= ` sec theta + tan^3 theta cosec theta`
= ` sec theta (1+ (tan^3 theta cosec theta)/(sec theta))`
= ` sec theta (1+ ( tan^3 theta) (cos theta)/(sin theta))`
= ` sec theta (1+ tan^3 theta cot theta )`
=` sqrt(1 + tan^2 theta) (1+ (tan^3 theta)/ (tan theta ))`
=` sqrt(1 + tan^2 theta) (1+ tan^2 theta)`
...
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