यदि `tantheta-cottheta=0` और `theta` धनात्मक न्यूनकोण कोण है तो `(tan(theta+15^(@)))/(tan(theta-15^(@)))` का मान क्या होगा?

Options

A. 3
B. `(1)/(3)`
C. `sqrt(3)`
D. `(1)/(sqrt(3))`

Answer

a

Explanation

`tan theta-cottheta=0`
Put `theta=45^(@)`
`tan45^(@)-cot45^(@)=0`
`1-1=0`
0=0 (satisfied)
So, `theta=45^(@)`
Now ,`(tantheta+15^(@))/(tantheta-45^(@))`
`rArr(tan(45^(@)+15^(@)))/(tan(45^(@)-15^(@)))`
`rArr(tan60^(@))/(tan30^(@))rArrsqrt(3)/(1)/sqrt(3)=sqrt(3)xxsqrt(3)=3`