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(sqrt2-sin25^(@)-cos25^(@))/(sin25^(@)-c...

`(sqrt2-sin25^(@)-cos25^(@))/(sin25^(@)-cos25^(@))` is equal to

A

`tan 25^(@)`

B

`cos20^(@)`

C

`-tan10^(@)`

D

`sec 10^(@)`

Text Solution

Verified by Experts

`(sqrt2-sqrt2((1)/(sqrt2)sin25^(@)+(1)/(sqrt2)cos25^(@)))/(sqrt2(1-cos25^(@)-(1)/(sqrt2)cos25^(@)))=(sqrt2-sqrt2cos(25^(@)-45^(@)))/(sqrt2sin(25^(@)-45^(@)))`
`=(sqrt2(1-cos20^(@)))/(sqrt2sin(-20^(@)))=(2sin^(2)10^(@))/(-2sin10^(@)cos10^(@))=-tan10^(@)`
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