Question

sin 30° + tan 45º - cosec 60°/
sec 30° + cós 60° + cot 45°​

Answer 1

Given :-

(sin30° + tan45° - cosec60°)/(sec30° + cos60° + cot45°)

We know that,

• sin30° = 1/2

• tan45° = 1

• cosec60° = 2/√3

• sec30° = 2/√3

• cos60° = 1/2

• cot45° = 1

Therefore (sin30° + tan45° - cosec60°)/(sec30° + cos60° + cot45°) :-

= (1/2 + 1 - 2/√3)/(2/√3 + 1/2 + 1)

$\sf = \frac{ \frac{ \sqrt{3} }{2 \sqrt{3} } + \frac{2 \sqrt{3} }{2 \sqrt{3} } - \frac{4}{2 \sqrt{3} } }{ \frac{4}{2 \sqrt{3} } + \frac{ \sqrt{3} }{2 \sqrt{3} } + \frac{2 \sqrt{3} }{2 \sqrt{3} } } \\ \\ \sf = \frac{ \frac{3 \sqrt{3} - 4 }{2 \sqrt{3} } }{ \frac{3 \sqrt{3 } + 4 }{2 \sqrt{3} } } \\ \\ \sf = \frac{3 \sqrt{3} - 4}{2 \sqrt{3} } \times \frac{2 \sqrt{3} }{3 \sqrt{3} + 4} \\ \\ \sf = \frac{3 \sqrt{3} - 4 }{3 \sqrt{3} + 4}$

By rationalizing, we get

= (43 - 24√3)/11

Hence, the value of (sin 30° + tan 45º - cosec 60°)/(sec 30° + cos 60° + cot 45°) is (43 - 24√3)/11