Question

evaluate cos45°
______
sec30°+cosec60°
​

Answer 1

Answer:

√3/4√2

Step-by-step explanation:

Cos45°=1/√2

sec30°=2/√3

cosec60°=2/√3

1/√2

_________

2/√3+2/√3

=1/√2

_______

4/√3

= 1/√2×√3/4 = √3/4√2

Answer 2

$\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\red{W}\green{E}\purple{R}}}$

$\huge \: \frac{ \cos45° }{ \sin30° + \csc60° }$

As we know;

$\large \cos45° = \frac{1}{ \sqrt{2} }$

$\large \ \sec 30° = \frac{2}{ \sqrt{3} }$

$\large \csc60° = \frac{2}{ \sqrt{3} }$

Now let us evaluate -

$\large = \ \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} + \frac{2}{ \sqrt{3} } } }$

$\large \: = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2 + 2}{ \sqrt{3} } }$

$\large = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{4}{ \sqrt{3} } }$

$\large= \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2}$

$\large= \frac{ \sqrt{3} }{4 \sqrt{2} }$

Therefore;

$\huge \: \frac{ \cos45° }{ \sin30° + \csc60° } = \frac{ \sqrt{3} }{4 \sqrt{2}}$

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$\large\bf{\underline{\purple{Hope \: It \: Helps \: You!}}}$