Question : If sinθ + cosθ = √3, then the value of tanθ + cotθ is
a) 0
b) 1
c) 2
d) none of the other.
Doubt by Zoha
Solution :
sinθ + cosθ = √3
Squaring Both Sides (SBS)
(sinθ + cosθ)2 = (√3)2
sin2θ + cos2θ + 2sinθcosθ = 3
sin2θ + cos2θ + 2sinθcosθ = 3
1 + 2sinθcosθ = 3
[∵ sin2θ + cos2θ = 1]
2sinθcosθ = 3-1
2sinθcosθ = 2
sinθcosθ = 2/2
sinθcosθ = 1 — (1)
Now,
=tanθ + cotθ
Hence, b) would be the correct option.