Question

The value of \[\frac{\tan 55°}{\cot 35°}\] + cot 1° cot 2° cot 3° .... cot 90°, is

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Answer 1

We have to find the value of the following expression 

`(tan 55°)/(cot 35°)+cot 1° cot 2° cot 3°.......cot 90°` 

= `(tan 55°)/(cot 35°)+cot 1° cot 2° cot 3° ........ cot 90°` 

`= tan (90°-35°)/cot 35°+cot (90°-89°)cot (90°-88°)cot(90°-87°)°......cot 87 cot 88 cot 89........ cot 90°` 

`= (cot 35°)/(cot 35°)+tan 89° tan 88° tan 87°...... cot 87° cot 88° cot 89°.......cot 90°`  

=` 1xx1xx1xx1........xx0` 

`= 1 `

`"As cot " 90°=0`