1anothr way cud be 2 tke cosθ as x..treat it as quadratc..find minima...x comes out 2 b -1/2...
so min value= 2(-1/2)2 + 2(-1/2) -1= -3/2....
Cos 2θ + 2cosθ is always
1) greater than -3/2
2) less than or equal to 3/2
3) greater than or equal to -3/2
4) none of these
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3 Answers
1i think in the expression
2cos2θ - 1+ 2cosθ
min value of cosθ is -1 and that of cos2θ is 0
so min value will be -3
iso ans is (1)
1Cos 2θ + 2cosθ = 2cos2θ + 2cosθ -1
=2[cos2θ+cosθ-1/2]
=2[ (cosθ+1/2)2 -1/4 -1/2 ]
=2(cosθ+1/2)2-3/2 ≥ -3/2 for all θ
this was the ans. given
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