Question

the value of cos15× cos 45+2 cosec75​

Answer 1

Step-by-step explanation:

$cos15×cos 45+2cosec75 \\ =( \frac{ \sqrt{3 } + 1}{2 \sqrt{2} } )( \frac{1}{ \sqrt{2} } ) + \frac{2}{sin75} \\ = \frac{ \sqrt{3} + 1}{4} + \frac{2}{cos(90 - 75)} \\ = \frac{ \sqrt{3} + 1}{4} + \frac{2}{cos15} \\ = \frac{ \sqrt{3} + 1 }{4} + \frac{2}{ \frac{ \sqrt{3} + 1}{2 \sqrt{2} } } \\ = \frac{ \sqrt{3} + 1}{4} + \frac{4 \sqrt{2} }{ \sqrt{3} + 1} \\ = \frac{ ( \sqrt{3} + 1)( \sqrt{3} + 1) + 16 \sqrt{2} }{(4)( \sqrt{3} + 1)} \\ = \frac{3 + 2 \sqrt{3 } + 1 + 16 \sqrt{2} }{4 \sqrt{3} + 4 } \\ = \frac{4 + 16 \sqrt{2} + 2 \sqrt{3}}{4 + 4 \sqrt{3} }$