Question

Show that "1-2sin theta cos theta>=0" for all "theta in R

Answer 1

Answer:

1 - 2SinθCosθ ≥ 0

Step-by-step explanation:

Show that "1-2sin theta cos theta>=0"

We need to show that

1 - 2SinθCosθ ≥ 0

As we know that Sin2θ = 2SinθCosθ

if  1 - Sin2θ ≥ 0

if   -Sin2θ  ≥ - 1

if  Sin2θ ≤  1

Which is true

other way

1 - 2SinθCosθ

as we know that Cos²θ + Sin²θ = 1

= Cos²θ + Sin²θ - 2SinθCosθ

= (Cosθ - Sinθ)²

and square of any number ≥ 0

=> (Cosθ - Sinθ)² ≥ 0

=> 1 - 2SinθCosθ ≥ 0

Answer 2

Answer:

the answer is theta lies between 0 to 2