# If tanθ + cotθ = 4/√3, where 0 < θ < π/2, then sinθ + cosθ is equal to

(a) 1

(b) (√3 – 1)/2

(c) (√3 + 1)/2

(d) √2

**Answer: (c) (1 + √3)/2 **

**Solution:-**

tanθ + cotθ = 4/√3

tanθ + 1/tanθ = 4/√3

= (tan²θ + 1)/tanθ

**As we know that tan²θ + 1 = sec²θ**,

Then, sec²θ/tanθ = 4/√3

cosθ/cos²θ sinθ = 4/√3

1/cosθ sinθ = 4/√3

Multiply and divide by 2,

Then, 2/2cosθ sinθ = 4/√3 **(sin2θ = 2 sinθcosθ)**

1/sin2θ = 2/√3

Then, sin2θ = √3/2

sin2θ = sin60º

2θ = 60

θ = 60/2 => θ = 30º

So, the value of Sinθ + cosθ = sin30º + cos30º

1/2 + √3/2 = (1 + √3)/2

Hence, the correct answer is option (c) (1 + √3)/2.