Question

cos 2ɵ + 2 cos ɵ is always

Answer 1

Answer:

We have,

cos2θ+2cosθ=2cos

2

θ−1+2cosθ=2(cosθ+

2

1

)

2

−

2

3

Now, 2(cosθ+

2

1

)

2

≥0 for all θ

∴2(cosθ+

2

1

)

2

−

2

3

≥

2

−3

for all θ

⇒cos2θ+2cosθ≥

2

−3

for all θ

Also, maximum value of this expression is 3