Is 2-csc^2(θ)=1+cot^2(θ) ?

The answer to whether 2-csc^2(θ)=1+cot^2(θ) is False

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prove 2-csc^2(θ)=1+cot^2(θ)

prove

2 - csc^{2} (θ) = 1 + cot^{2} (θ)

False

Solution steps

2 - csc^{2} (θ) = 1 + cot^{2} (θ)

Show that the two sides are not equal

For

2 - csc^{2} (θ) = 1 + cot^{2} (θ)

plug in

θ = 1

2 - csc^{2} (1) = 0.58771 \dots

2 - csc^{2} (1)

Refine to a decimal form

= 0.58771 \dots

1 + cot^{2} (1) = 1.41228 \dots

1 + cot^{2} (1)

Refine to a decimal form

= 1.41228 \dots

The two sides are not equal

\Rightarrow False

sin (\frac{π}{6} + b) + cos (\frac{π}{3} + b) = cos (b)

cos^{2} (x) - sin^{2} (x)

1 - cos^{2} (x)

1 - sin^{2} (x)

sin (2 θ)