Correct Answer - Option 3 : -4

**Concept:**

sec (360° - θ) = sec θ;

cosec (180° + θ) = - cosec θ

**Calculation:**

\(\rm cosec\left(\dfrac{7\pi}{6}\right)sec\left(\dfrac{5\pi}{3}\right)\)

= cosec (210^{∘}) sec (300^{∘})

= cosec(180^{∘} + 30^{∘}) sec(360^{∘} - 60^{∘})

= - cosec 30^{∘} sec 60∘

= - 2 (2)

= - 4

sin (360° - θ) = - sin θ

cos (360° - θ) = cos θ

tan (360° - θ*) *= - tan θ

cosec (360° - θ) = - cosec θ

sec (360° - θ) = sec θ

cot (360° - θ*) *= - cot θ

sin (180° + θ) = - sin θ

cos (180° + θ) = - cos θ

tan (180° + θ) = tan θ

cosec (180° + θ) = -cosec θ

sec (180° + θ) = - sec θ

cot (180° + θ) = cot θ

sin (90° - θ) = cos θ

cos (90° - θ) = sin θ

tan (90° - θ) = cot θ

cosec (90° - θ) = sec θ

sec (90° - θ) = cosec θ

cot (90° - θ) = tan θ