यदि `tan theta + sec theta = 4 ` हो , तो ` sin theta` का मान क्या है ?

Options

A. `8//17`
B. ` 8//15`
C. `15//17`
D. `23//32`

Answer

C

Explanation

चूंकि ` tan theta + sec theta = 4`
` rArr (sintheta)/(costheta) + 1/(costheta) = 4`

` rArr (1+sin theta)/(costheta) = 4`






` rArr ( cos theta //2 + sin theta//2)^(2)/((cos theta//2 + sin theta//2))=4`
` ( cos theta //2 - sin theta//2)`


` rArr (costheta//2 + sin theta//2)/(cos theta//2 - sin theta//2)=4`

` rArr ( 1+ tan theta//2 )/(1-tan theta//2)=4`

` rArr 1 + tan theta//2 = 4 -4 tan theta //2`

` rArr 5 tan theta//2 = 3`
` rArr tan theta //2 = 3//5 " " ` ...(i)
चूंकि ` sin theta = ( 2 tan theta //2 )/(1+ tan^(2) theta//2 )`

`= (2*3 //5)/(1+(9//25))`

` = (6//5)/(34//25)`

` = 30/34= 15/17`