sinA + cosA = √2. Evaluate tanA + cotA
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On squaring both sides, we get
(sinA + cosA)^2 = (root)^2
We know that (a + b)^2 = a^2 + b^2 + 2ab
sin^2A + cos^2A + 2sinAcosA = 2
1 + 2sinAcosA = 2
2sinAcosA = 1
We know that 2sinAcosA = sin2A
sin2A = sin90
2A = 90
A = 45.
Now,
Tan A + cotA = Tan(45) + cot(45)
= 1 + 1
= 2.
Hope this helps!
squaring both sides we get
2sinAcosA =1. sinACosA=1/2
then tanA +cotA = sinA/cosA +cosA/sinA
=sin^2A +cos^2A)/sinA×cosA
=1/(1/2)
=2