`(2sin68^(@))/(cos22^(@))-(2cot15^(@))/(5tan75^(@))-(3tan45^(@).tan20^(@).tan40^(@).tan50^(@).tan70^(@))/(5)` is equal to

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

c

Explanation

`(2sin68^(@))/(cos22^(@))-(2cot15^(@))/(5tan75^(@))`
`(3tan45^(@).tan20^(@).tan40^(@).tan50^(@).tan70^(@))/(5)`
`rArr(2sin68^(@))/(cos(90^(@)-68^(@))/(cos(90^(@)-68^(@)))-(2cot15^(@))/(5tan(90^(@)-15^(@)))-(3xx1(tan20^(@).tan70^(@))(tan40^(@).tan50^(@)))/(5)`
`rArr(2sin68^(@))/(sin68^(@))-(2cot15^(@))/(5cot15^(@))-(3xx1xx1xx1)/(5)`
`(tanA.tanB=1"if"A+B=90^(@))`
`rArr2-(2)/(5)-(3)/(5)=1`