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tan54^(@) can be expressed as...

`tan54^(@)` can be expressed as

A

`(sin9^(@)+cos9^(@))/(sin9^(@)-cos9^(@))`

B

`(sin9^(@)-cos9^(@))/(sin9^(@)+cos9^(@))`

C

`(cos9^(@)+sin9^(@))/(cos9^(@)-sin9^(@))`

D

`(sin36^(@))/(cos36^(@))`

Text Solution

Verified by Experts

The correct Answer is:
C
`tan54^(@)=tan(45^(@)+9^(@))`
`=(tan45^(@)+tan9^(@))/(1-tan45^(@)*tan9^(@))=(1+tan9^(@))/(1-tan9^(@))`
`=(1+(sin90^(@))/(cos9^(@)))/(1-(sin9^(@))/(cos90^(@)))=(cos9^(@)+sin9^(@))/(cos9^(@)-sin9^(@))`
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