1.

If 1/6 sintheta, costheta and tantheta are in G.P. then the general solution for theta is-

Answer»

`2npi+-pi/3`
`2npi+-pi/6`
`npi+-pi/3`
none of these

Solution :Since, `1/6sintheta,COSTHETA, tantheta` are in G.P.
`RARR COS^(2)theta=1/6(sintheta.tantheta) rArr 6cos^(3)theta+cos^(2)theta-1=0`
`therefore (2costheta-1)(3 cos^(2)theta+2costheta+1)=0`
`rArr costheta=1/2` (other VALUES of `costheta` are imaginary)
`rArr costheta=cospi/3 rArr theta=2npi+-pi/3, N in I`.


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