InterviewSolution
Saved Bookmarks
| 1. |
Consider the equation sectheta+ cottheta = 31/12 On the basis of above, answer the following Number of values of theta where theta in [0,5pi] is equal to |
|
Answer» `4` `implies (1+t^(2))/(1-t^(2))+(1-t^(2))/(2t)=(31)/(12)` `implies6t^(4)+43t^(3)-12t^(2)-19t+6=0` `implies(3t-1)(2t^(3)+15t^(2)+t-6)=0` `implies t=(1)/(3),alpha,beta,gamma` where `alpha in(-8,-7)implies(theta)/(2)in((pi)/(2),(3pi)/(4))` `beta in (-1,(-1)/(2))implies(theta)/(2) in ((3pi)/(4),(7pi)/(8))` `gamma in((1)/(2),1)implies(theta)/(2)in(0,(pi)/(4))` (i) if `0lttheta lt (pi)/(2)` then `t=(1)/(3)` or `t in ((1)/(2),1)` `implies tan theta =(3)/(4) "or if" tan. (theta)/(2)in((1)/(2),1)implies "tan" theta in ((4)/(3),oo)` `implies"Min value of" [tan theta] =0` (ii)No. of values of `theta in ((pi)/(2),(3pi)/(2))`will be 1 |
|