`(tantheta)(1+sec2theta)(1+sec4theta)(1+sec8theta)`का मान कितना होगा ?

Options

A. `tan10theta`
B. `tan8theta`
C. `tan12theta`
D. 1

Answer

b

Explanation

`tan theta(1+sec2theta)(1+sec 4 theta)`
`(1+sec 8 theta)`
Put, `theta= 30^(@)`
`tan 30^(@)(1+sec6 0^(@))(1+sec120^(@))`
`(1+sec240^(@))`
`rArr(1)/sqrt(3)(1+2)(1-2)(1-2)`
`rArr(1)/sqrt(3)xx3xx(-1)(-1)=sqrt(3)`
Now, take option (b)
`tan 8 theta=tan 240 ^(@)`
`=tan (180^(@)+60^(@))`
`=tan 60^(@)`
`=sqrt(3)`