The value of `2tanpi/(10)+3secpi/(10)-\ 4cospi/(10)` is `0` b. `1` c. `sqrt(5)` d. none of these

Explanation

`a=2tanpi/(10)+3secpi/(10)-\ 4cospi/(10)`

`a=frac{2sin frac{pi}{10}+3-4cos^2 frac{pi}{10}}{cos frac{pi}{10}}`

`a=frac{2 sin frac{pi}{10}cos frac{pi}{10}-(4cos^3 frac{pi}{10}-3cos frac{pi}{10})}{cos^2 frac{pi}{10}}`

Knowing that, `2 sin xcos x=sin 2x` and `cos 3x=4cos^3 x-cos x`

`a=frac{sin frac{pi}{5}-cos frac{3 pi}{10}}{cos^2 frac{pi}{10}}`

`a=frac{sin frac{pi}{5}-sin(frac{pi}{2}-frac{3pi}{10})}{cos^2 frac{pi}{10}}=frac{sin frac{pi}{5}-sin{pi}{5}}{cos^2 frac{pi}{10}}`

`:. a=0`