Question

cos 45°/sec30°+cosec60°​

Answer 1

Answer:

$3 \sqrt{3 } \div 2 \sqrt{2}$

Answer 2

Step-by-step explanation:

we know that,

i) cos45° = 1/√2

ii) sec30° = 2/√3

iii ) cosec30° = 2/√3

______________________

Now ,

Value of

\frac{cos45°}{sec30+cosec60}

sec30+cosec60

cos45°

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

3

2

+

3

2

2

1

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

3

4

2

1

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

4

2

3

/*Rationalising the denominator, we get

=\frac{\sqrt{3}\times \sqrt{2}}{4\sqrt{2}\times\sqrt{2}}=

4

2

×

2

3

×

2

= \frac{\sqrt{6}}{8}=

8

6

Therefore,

\frac{cos45°}{sec30+cosec60} =\frac{\sqrt{6}}{8}

sec30+cosec60

cos45°

=

8

6

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