SSC CPO 2024 PYQ — Question 115

The correct answer is Option 3 i.e. $1 \over \sqrt3$.

tan(t) + cot(t) = 1

⇒ sin t/cos t + cot t/ sin t = 1   [tan(t) = sint/cost]

⇒ (sin²t + cos²t)/sin t cos t = 1

⇒ sin t cos t = 1

Now,

⇒ (sin t + cos t)² = sin²t + cos²t + 2 sint cos t

⇒ (sin t + cos t)² = 1 + 2 × 1    [sin²t + cos²t = 1]

⇒ (sin t + cos t)² = 3

⇒ (sin t + cos t) = $\sqrt3$

Thus, the value of $1 \over{sin(t) + cos(t)}$ = $1 \over \sqrt3$