Sec theta- tan theta =a then show that sec theta = 1/2(a+1/a)
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sec^2 theta - tan^2 theta = 1
tan^2 theta= sec^2 theta-1
sec theta - √ sec^2 theta -1 = a
(sec theta -a)^2 = sec^2 theta -1
sec^2 theta + a.a - 2a sec the ta = sec^2 theta -1
a.a - 2a sec theta = -1
sec theta= a.a +1)/2a
= 1/2 ( a+1/a)
tan^2 theta= sec^2 theta-1
sec theta - √ sec^2 theta -1 = a
(sec theta -a)^2 = sec^2 theta -1
sec^2 theta + a.a - 2a sec the ta = sec^2 theta -1
a.a - 2a sec theta = -1
sec theta= a.a +1)/2a
= 1/2 ( a+1/a)
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