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Question
The value of \[\frac{\tan 55°}{\cot 35°}\] + cot 1° cot 2° cot 3° .... cot 90°, is
Options
−2
2
1
0
Solution
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`
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