Question

Prove that sec theta + cos theta can never be equal to 3/2

Answer 1

Answer:

How can you prove that sec theta+cos theta is not equal to 3/2?

Well let’s try to find out what happens if it can be equal to 3/2

We will have

secθ+cosθ=32⟺

1cosθ+cosθ=32⟺

1+cos2θ=3cosθ2⟺

2+2cos2θ=3cosθ⟺

2cos2θ−3cosθ+2=0

The above equation has no real solutions for cosθ since the discriminant of the quadratic equation is

Δ=(−3)2–4⋅2⋅2=9−16=−7<0

So there is non way secθ+cosθ=32

therefore

secθ+cosθ≠32