1.

Solve the equation 4costheta+5sintheta=5 if tan51^(@)21^(')=5/4

Answer»

Solution :Let `theta=51^(@)21^(')`
`THEREFORE tantheta=5/4`
`rArr sintheta=5/sqrt(41)` and `cosphi=4/sqrt(41)`
Now `4costheta+5sintheta=5`
Divide both sides by `sqrt(4^(2)+5^(2))=sqrt(41)`
`4/sqrt(41) costheta+5/sqrt(41)sintheta=5/(sqrt(41))`
`rArr COS(theta-phi)=cos(pi/2-phi)`
`rArr (theta-phi)=2NPI+-(pi/2-phi)`
Taking positive SIGN
`(theta-phi)=2npi+(pi/2-phi)`
`rArr theta=2npi+pi/2` Ans.
Taking negative sign
`(theta-phi)=2npi-(pi/2-phi)`
`rArr theta=2npi-(pi/2-theta)`
`rArr theta=2npi-pi/2+2theta`
`rArr theta=2npi-90^(@)+2 xx 51^(@)21^(')`
`=2npi-90^(@)+102^(@)42^(')`
`=2npi+12^(2)42^(')` Ans.


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