Question

sec theta+tan theta=p then the value of p square
+1/p square-1

Answer 1

sec theta+tan theta=p
squaring both the sides
(sec theta)^2+(tan theta)^2=p^2
1^2=p^2
p=1

Answer 2

putting the value of p in the question

=(sec theta + tan theta)2 +/ (sec theta + tan theta)2-1

=sec2 theta +2 sec theta tan theta + tan2 theta +1/ sec2 theta + 2 sec theta ta theta -1

we know that sec theta - tan theta is 1

so putting its value

sec2 theta + 2 sec theta tan theta + tan2 theta +(sec2 theta - tan2 theta)/sec2 theta + 2 sec theta tan theta + tan2 theta  -(sec2 theta - tan2 theta)

sec2 theta + 2 sec theta tan theta + sec2 theta/tan2 theta + 2 sec theta tan theta + tan2 theta

taking sec in the numerator as common

and tan as common in denominator

2 sec theta ( sec theta + tan theta )/ 2  tan theta ( tan theta + sec theta )

cutting tan theta + sec theta

2 sec theta /2 tan theta

= cosec theta

hence proved

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