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
