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cot16^0cot44^0+cot44^0cot76^0-cot76^0cot...

`cot16^0cot44^0+cot44^0cot76^0-cot76^0cot16^0=` 1 (b) 2 (c) 3 (d) 4

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`(cos16^(@)cos44^(@))/(sin16^(@)sin44^(@))-1+(cos44^(@)cos76^(@))/(sin44^(@)sin76^(@))-1-(cos76^(@)cos16^(@))/(sin76^(@)sin16^(@))-1+3`
`=(cos60^(@))/(sin16^(@)sin44^(@))+(cos120^(@))/(sin44^(@)sin76^(@))-(cos60^(@))/(sin76^(@)sin16^(@))+3`
`=(1)/(2)((2sin30^(2)cos46^(@))/(sin16^(@)sin44^(@)sin76^(@)))-(1)/(2sin76^(@)sin16^(@))+3`
`=(1)/(2)((2sin30^(@)sin44^(@))/(sin16^(@)sin44^(@)Sin76^(@)))-(1)/(2sin76^(@)sin16^(@))+3`
`=3`
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