Question

cot30/sec30+cosec30/tan45-2cos0/30+cos^245 without using table​

Answer 1

Given :

$\frac{cot 30 }{sec 30} + \frac{cosec 30 }{tan 45} - \frac{2 cos 0} { sin 30 } + cos^{2} 45$

solution :

The given question cannot be solved without using the table.

Firstly write down all the values which are  needed  :

cot 30° = $\sqrt{3}$

sec 30° = $\frac{2}{\sqrt{3} }$

cosec 30° = 2

cos 0° =  1

cos 45° =  $\frac{1}{\sqrt{2} }$

tan 45° = 1

sin 30° = $\frac{1}{2}$

Now substitute all the values :

$\frac{cot 30 }{sec 30} + \frac{cosec 30 }{tan 45} - \frac{2 cos 0} { sin 30 } + cos^{2} 45$

⇒ $\frac{\sqrt{3} }{\frac{2}{\sqrt{3} } } + \frac{2}{1} - \frac{2 (1)}{\frac{1}{2} } + (\frac{1}{\sqrt{2} }) ^{2}$

By solving we get

⇒ $\frac{3}{2} + 2 - 2 + \frac{1}{2}$

By cancelling +2 and -2 we get

⇒$\frac{3}{2} + \frac{1}{2}$

⇒$\frac{4}{2}$

⇒$2$

Therefore ,  $\frac{cot 30 }{sec 30} + \frac{cosec 30 }{tan 45} - \frac{2 cos 0} { sin 30 } + cos^{2} 45$ = 2