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The value of cot70^(@)+4cos70^@ is...

The value of `cot70^(@)+4cos70^@` is

A

`(1)/(sqrt(3))`

B

`sqrt(3)`

C

`2sqrt(3)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Now, `cot70^(@)+4cos70^(@)`
`=(cos70^(@)+4sin70^(@)cos70^(@))/(sin70^(@))`
`=(cos70^(@)+2sin140^(@))/(sin70^(@))`
`(cos70^(@)+2sin(180^(@)-40^(@)))/(sin70^(@))`
`=(sin20^(@)+sin40^(@)+sin40^(@))/(sin70^(@))`
`=(2sin30^(@)cos10^(@)+sin40^(@))/(sin70^(@))`
`=(sin80^(@)+sin40^(@))/(sin70^(@))`
`=(2sin60^(@)cos20^(@))/(sin70^(@))`
`=sqrt(3)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-FACTORIZATION FORMULAE -EXERCISE 2
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