the value of `tan9^@-tan2 7^@-tan6 3^@+tan8 1^@` is equal to

Options

A. 1
B. 2
C. 3
D. 4

Answer

D

Explanation

Given expression is `tan9-tan27^(@)-tan63^(@)+tan81^(@)`
`=tan9^(@)-tan27^(@)-tan(90^(@)-27^(@))+tan(90^(@)-9^@)`
`=tan9^(@)-tan27^(@)-cot27^(@)+cot9^(@)`
`=(tan9^(@)+cot9^(@))-(tan27^(@)+cot27^(@))`
`=(1)/(sin9^(@)cos9^(@))-(1)/(sin27^(@)cos27^(@))`
`=(2)/(sin18^(@))-(2)/(sin54^(@))`
`=(2)/(sin18^(@))-(2)/(sin(90^(@)-36^(@)))`
`=(2)/(sin18^(@))-(2)/(cos36^(@))`
`=2[(4)/(sqrt(5)-1)-(4)/(sqrt(5)+1)]=8xx(2)/(4)=4`
(By putting value of sin `18^(@) and cos 36^(@))`