Question

find the value of cos45/sec 30 + cosec 30

Answer 1

Answer:

Step-by-step explanation:

Cos45= 1/√2

Sec30=2/√3

Cosec30=2/1

1/√2 x √3/2 +2

√3/2√2+2

√3/2√2+2√2(2)/2√2

4√2√3/2

2√2√3

Answer 2

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