Question

Evaluate - cos 45°/sec30°+cosec30°​

Answer 1

Step-by-step explanation:

Let's write the values first.

cos 45 = 1 / root 2

sec 30 = 2 / root 3

cosec 30 = 2

Therefore,

(cos45) ÷ (sex 30 + cosec 30) = (1/root2) ÷ (2/root30 + cosec30)

= root 3 / 2root2 + 2root6

conjucating,

= - (root6 - 4 root2) / 8

Answer 2

$\frac{cos45 \degree}{sec30 \degree + cosec30 \degree} \\ \\ = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} } + 2 } \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{ 2 + 2 \sqrt{3} } \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} + 2 \sqrt{6} } \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} + 2 \sqrt{6} } \times \frac{2 \sqrt{2} - 2 \sqrt{6} }{2 \sqrt{2} - 2 \sqrt{6} } \\ \\ = \frac{2 \sqrt{6} - 2 \sqrt{18} }{8 - 24} \\ \\ = \frac{2 \sqrt{6} - 6 \sqrt{2} }{ - 16} \\ \\ = \frac{3 \sqrt{2} - \sqrt{6} }{8}$