Question

$\sin(30) + \tan(45) - \csc(60) \div \sec(30) \div \cos(60) - \cot(45)$
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Answer 1

sin(30) + tan(45) - cosec(60)

———————————————

sec(30) + cos(60) + cot(45)

= 1/2 + 1 - 2/√3. 3/2 - 2/√3. (3/2 - 2/√3)

——————— = —————— × ——————

2/√3 + 1/2 + 1. 3/2 + 2/√3 (3/2 - 2/√3)

= 9/4 - 2 × 3/2 × 2/√3 + (2/√3)2

———————————————

(3/2)2 - (2/√3)2

(27 - 24√3 + 16)

————————

= 9/4 - 2√3 + 4/3. 12

———————— = ————————

9/4 - 4/3. 27 - 16

————————

12

= 43 - 24√3

——————

11

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