Question

3 cos^260^o + 2 cot^2
30^o - 5 sin^245^o = ?​

Answer 1

3 cos^2(60°) + 2cot^2 (30°) - 5sin^2(45°)

3(1/2)^2 + 2{cos^2(30°)/sin^2(30°)}-5(1/√2)^2

3(1/4) + 2{(√3/2)^2/(1/2)^2} - 5(1/2)

3/4 + 2{ (3/4)/(1/4)} - 5/2

3/4 + 2 {3} - 5/2

3/4 + 6 - 5/2

(3 + 24 - 10)/4 { taking LCM }

17/4 is the answer