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2sin2 x

2(1 - cos2 x) = 2 + cos x

2 - 2cos2 x = 2 + cos x

- 2cos2 x - cos x = 0

cos x(-cos x - 1) = 0

cos x = 0 or -cos x - 1 = 0

cos x = -1

Since the cosine has a period of 2pi, in the interval 0 â‰¤ x â‰¤ 2pi

when cos x = 0, x = pi/2 and x = 3pi/2, and

when cos x = -1, x = pi.

All values of x that satisfy the given equation are:

x = pi/2 + 2npi, x = pi +2npi, and x = 3pi/2+ 2npi where n is any integer.

Q: What is the work for 2 sin squared x equals 2 plus cos x?

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No, (sinx)^2 + (cosx)^2=1 is though

Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.

1. Anything divided by itself always equals 1.

1

The deriviative of sin2 x + cos2 x is 2 cos x - 2 sin x

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No, (sinx)^2 + (cosx)^2=1 is though

Until an "equals" sign shows up somewhere in the expression, there's nothing to prove.

22

1. Anything divided by itself always equals 1.

2 x cosine squared x -1 which also equals cos (2x)

sin cubed + cos cubed (sin + cos)( sin squared - sin.cos + cos squared) (sin + cos)(1 + sin.cos)

Multiply both sides by sin(1-cos) and you lose the denominators and get (sin squared) minus 1+cos times 1-cos. Then multiply out (i.e. expand) 1+cos times 1-cos, which will of course give the difference of two squares: 1 - (cos squared). (because the cross terms cancel out.) (This is diff of 2 squares because 1 is the square of 1.) And so you get (sin squared) - (1 - (cos squared)) = (sin squared) + (cos squared) - 1. Then from basic trig we know that (sin squared) + (cos squared) = 1, so this is 0.

No. Cos squared x is not the same as cos x squared. Cos squared x means cos (x) times cos (x) Cos x squared means cos (x squared)

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2

The deriviative of sin2 x + cos2 x is 2 cos x - 2 sin x

There is a hint to how to solve this in what is required to be shown: a and b are both squared.Ifa cos θ + b sin θ = 8a sin θ - b cos θ = 5then square both sides of each to get:a² cos² θ + 2ab cos θ sin θ + b² sin² θ = 64a² sin² θ - 2ab sin θ cos θ + b² cos² θ = 25Now add the two together:a² cos² θ + a² sin² θ + b² sin² θ + b² cos² θ = 89→ a²(cos² θ + sin² θ) + b² (sin² θ + cos² θ) = 89using cos² θ + sin² θ = 1→ a² + b² = 89