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The value of cot(7pi)/(16)+2cot(3pi)/8+c...

The value of `cot(7pi)/(16)+2cot(3pi)/8+cot(15pi)/(16)` is 4 (b) 2 (c) `-2` (d) `-4`

A

4

B

2

C

`-2`

D

`-4`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan((pi)/(2)-(7pi)/(16))+2tan((pi)/(2)-(3pi)/(8))-cot(pi-(15pi)/(16))`
`=tan((pi)/(16))-cot((pi)/(16))+2tan((pi)/(8))`
`=(sin((pi)/(16)))/(cos((pi)/(16)))-(cos((pi)/(16)))/(sin((pi)/(16)))+2tan((pi)/(8))`
`=-(2cos((pi)/(8)))/(sin((pi)/(8)))+2(sin((pi)/(8)))/(cos((pi)/(8)))=-(4cos((pi)/(4)))/(sin((pi)/(4)))=-4`
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