Correct Answer - Option 4 : 1/4
Calculation:
Given,
\(\sin \theta \cdot \cos \theta = \frac{1}{2}\)
⇒ 2 sin θ ⋅ cos θ = 1
⇒ sin 2θ = sin 90°
⇒ 2θ = 90° ⇒ θ = 45°
Take, sin6 θ + cos6 θ = sin6 45° + cos6 45°
\( = {\left( {\frac{1}{{\sqrt 2 }}} \right)^6} + {\left( {\frac{1}{{\sqrt 2 }}} \right)^6}\)
\( = \frac{1}{8} + \frac{1}{8} = \frac{1}{4}\)
