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Question
Prove the following identities:
`(sec theta + tan theta)/(sec theta - tan theta) = (sec theta + tan theta)^2 = 1 + 2 tan^2 theta + 2 sec theta tan theta`
Theorem
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Solution
Here, `(sec theta + tan theta ) /( sec theta - tan theta)`
=`((sec theta + tan theta ) ( sec theta + tan theta))/(( sec theta - tan theta ) ( sec theta + tan theta ))`
=` ((sec theta + tan theta )^2) /( sec^2 theta - tan^2 theta)`
=`((sec theta + tan theta )^2)/1`
=`(sec theta + tan theta )^2`
Again , `(sec theta + tan theta )2`
=` sec^2 theta + tan^2 theta + 2 sec theta tan theta `
=` 1+ tan^2 theta + tan^2 theta + 2 sec theta tan theta`
=`1+2 tan^2 theta + 2 sec theta tan theta `
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