Question

sec75° + cosec75° =
but i want answer in root form ​

Answer 1

Answer:

$\huge \mathfrak \pink{answer}$

$sec(75) \: = 3.863 \\ cosec(75) = 1.035 \\ sec(75) + cosec(75) = 4.898$

Answer 2

Answer:

hey here is your solution

pls mark it as brainliest

Step-by-step explanation:

$to \: find = \\ sec \: 75 + coseec \: 75 \\ \\ so \: we \: know \: that \\ cosec(90 - x) = sec \: x \\ \\ thus \: then \\ = sec \: 75 + cosec \: (90 - 75) \\ \\ = sec \: 75 + sec \: 15 \\ \\ = \frac{1}{cos \: 75} + \frac{1}{cos \:1 5} \\ \\ = \frac{1}{cos \: (45 + 30)} + \frac{1}{cos \: (45 - 30)} \\ \\ we \: know \: that \\ \\ cos(x + y) = cos \: x.cos \: y - sin \: x.sin \: y \\ \\ cos \: (x - y) = cos \: x.cos \: y + sin \: x.sin \: y$

$thus \: then \: accordingly \\ \\ = \frac{1}{(cos \: 45.cos \: 30) - (sin \: 45.sin \: 30)} + \frac{1}{(cos \: 45.cos \: 30 )+ sin \: 30.sin \: 45} \\ \\ = \frac{1}{ (\frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} \: ) - ( \frac{1}{ \sqrt{2} } \times \frac{1}{2} )} \: + \frac{1}{ (\frac{1}{ \sqrt{2} } \times \frac{ \sqrt{ 3} }{2} \: ) + ( \frac{1}{2} \times \frac{1}{ \sqrt{2} }) } \\ \\ = \frac{1}{ \frac{ \sqrt{3} }{2 \sqrt{2} } - \frac{1}{2 \sqrt{2} } } + \frac{1}{ \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } } \\ \\ = \frac{ \frac{1}{ \sqrt{3} - 1 } }{2 \sqrt{2} } + \frac{ \frac{1}{ \sqrt{ 3} + 1 } }{2 \sqrt{2} }$

$\frac{2 \sqrt{2} }{ \sqrt{3} - 1 } + \frac{2 \sqrt{2} }{ \sqrt{3} + 1 } \\ \\ = \frac{2 \sqrt{2}( \sqrt{3} + 1) + 2 \sqrt{2} ( \sqrt{3} - 1) }{( \sqrt{3} - 1)( \sqrt{3} + 1) } \\ \\ = \frac{2 \sqrt{6} + 2 \sqrt{2} + 2 \sqrt{6} - 2 \sqrt{2} }{( \sqrt{3}) {}^{2} - (1) {}^{2} } \\ \\ = \frac{4 \sqrt{6} }{(3 - 1)} \\ \\ = \frac{4 \sqrt{6} }{2} \\ \\ = 2 \sqrt{6}$