यदि `Axxtan(theta+150^(@))=Bxxtan(theta-60^(@)),(A-B)/(A+B)` का मान क्या होगा ?

Options

A. `-(sintheta)/(2)`
B. `(sin2theta)/(2)`
C. `(cos2theta)/(2)`
D. 0

Answer

a

Explanation

`Axx tan (theta+150^(@))=Bxxtan(theta-60^(@))`
`(A)/(B)=(tan(theta-60^(@)))/(tan(theta+150^(@)))`
put `theta=90^(@)`
`(A)/(B)=(tan(90^(@)-60^(@)))/(tan(90^(@) +150^(@)))`
` =(tan30^(@))/(tan(180^(@)+60^ (@)))=(tan30^(@))/(tan60^(@))`
`(A)/(B)=(1)/(3)`
then `(A+B)/(A-B)=-(4)/(2)`
`(A+B)/(A-B)=-2` ltb rgt `=(A-B)=-(1)/(2)`
Put in option (a)`-(sin90^(@))/(2)=-(1)/(2)`
So, option(s) is corr ect.