SOLUTION: (tan A + Cot A)^2 = Sec^ 2 A + Cosec^2 A prove this

Question 252449: (tan A + Cot A)^2 = Sec^ 2 A + Cosec^2 A prove this
Found 2 solutions by palanisamy, drk:
Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
(tanA+cotA)^2 = (tanA)^2+(cotA)^2+2*tanA*cotA
= (tanA)^2+(cotA)^2+2*tanA*(1/tanA)
=(tanA)^2+(cotA)^2+2
=1+(tanA)^2+1+(cotA)^2
=sec^2A+cosec^2A

Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
My general style is to turn things into sin and cos. I tell kids, we understand those better than the others. What have to do first is decide which side looks more complicated and turn it into the less complicated side. I will try to turn the left into the right. So,
(tan A + Cot A)^2 = Sec^ 2 A + Cosec^2 A
becomes
(sin A / cos A + cos A / Sin A)^2
Adding these fractions with common denominators gets us
(sin^2 A + cos^2 A) / (cos^2 A * Sin^2 A)
We have an identity in the numerator, so we now get
1 / (Cos^2 A * Sin^2 A)
This can be expressed as
1/cos^2 A + 1/sin^2 A
which then becomes
sec^2 A + cosec^2 A. This is the right hand side, so we are done.

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