Question

Question 3 Prove that (cot (π / 6))^2 + (cosec (5π / 6))^2 + 3(tan (π / 6))^2 = 6

Class X1 - Maths -Trigonometric Functions Page 73

Answer 1

LHS = cot²(π/6) + cosec(5π/6)+3tan²(π/6)
= cot²(π/6) + cosec(π -π/6)+3tan²(π/6)
= cot²(π/6) + cosec(π/6) + 3tan²(π/6)
= cot²(30°) + cosec(30°)+3tan²(30°)
= (√3)² + 2 + 3× (1/√3)²
= 3 + 2 + 1 = 6 = RHS