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Value of the expression (sec1 1^(@)sec1 ...

Value of the expression `(sec1 1^(@)sec1 9^(@)-2cot7 1^(@))/tan11^(@)` is equal to

A

`2 cot 11^(@)`

B

`tan 19^(@)`

C

`2 tan 11^(@)`

D

`(1)/(9)tan 19^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
`sec 11^(@).sec 19^(@)-2 cot 71^(@)`
`=(1)/(cos 11^(@)cos 19^(@))-(2 sin 19^(@))/(cos 19^(@))`
`=(1-2 sin 19^(@)cos 11^(@))/(cos 11^(@)cos 19^(@))`
`=(1-(sin 30^(@)+sin 8^(@)))/(cos 11^(@)cos 19^(@))`
`=(1-(1//2)-sin 8^(@))/(cos 11^(@)cos 19^(@))`
`=(sin 30^(@)-sin 8^(@))/(cos 11^(@)cos 19^(@))`
`=(2 sin 11^(@).cos 19^(@))/(cos 11^(@)cos 19^(@))`
`2 tan 11^(@)`
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