The value of `cottheta. Tantheta(90^(@)-theta)-sec(90^(@)-theta)co s ectheta+(sin^(2)25+sin^(2)65^(@))+sqrt(3)(tan45^(@)" "tan15^(@)tan30^(@).tan75^(@).tan85^(@))`.

Options

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

Answer

a

Explanation

`cottheta.tan(90^(@)-theta)-sec(90^(@)-theta)`
`co s ectheta+(sin^(2)25^(@)+sin^(2)65^(@))+sqrt(3)(tan5^(@).tan15^(@).tan30^(@).tan75^(@)tan85^(@))`.
`=cot theta.cottheta-co s ectheta.co s ectheta+(sin^(2)25^(@)+cos^(2)25^(@))+sqrt(3)(tan5^(@)tan85^(@)).(tan15^(@),tan^(2)75^(@)).tan30^(@))`
`(cot^(2)theta-co s ec^(2)theta)+(1)+sqrt(3)(1)`
` 1 .(1)/sqrt(3)[tanA.tanB=1 "if"A+B=90^(@)]`
`=(-1)+(1)+ sqrt(3)-(1)/sqrt(3)=-1-1+1 `
=1