SSC CPO 2024 PYQ — Question 134

The correct answer is option 3 i.e. 1.

Given that, sin⁴θ + cos⁴θ = 2sin²θcos²θ

Solving the given expression by value putting, 

Putting θ = 45°, sin⁴(45°) + cos⁴(45°) = 2sin²(45°)cos²(45°)

Now, sin(45°) = cos(45°) = $1 \over \sqrt{2}$

⇒ $({1 \over \sqrt{2}})^4 + ({1 \over \sqrt{2}})^4 = 2({1 \over \sqrt{2}})^2({1 \over \sqrt{2}})^2$

⇒ ${1 \over 2} = { 1\over 2}$  

⇒ θ = 45° satisfies the given equation,

So, cot(45°) = 1

Hence the value of cotθ is 1.