The answer to whether 1-sin(x)=cot(x) is False

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prove 1-sin(x)=cot(x)

Solution

prove

1 - sin (x) = cot (x)

False

Solution steps

1 - sin (x) = cot (x)

Show that the two sides are not equal

For

1 - sin (x) = cot (x)

plug in

x = 1

1 - sin (1) = 0.15852 \dots

1 - sin (1)

Refine to a decimal form

= 0.15852 \dots

cot (1) = 0.64209 \dots

cot (1)

Refine to a decimal form

= 0.64209 \dots

The two sides are not equal

\Rightarrow False

4 cos^{2} (θ) + 4 sin^{2} (θ) = 4

\frac{- cos ^{2} ( 2 θ )}{2} = \frac{- 1 - cos ( 4 θ )}{8}

\frac{1 - cos ( x )}{- 1 + sec ( x )} = cos (x)

2 sin (y) cos (y) sec (2 y) = tan (2 y)

sec (x) + tan (x) = \frac{1}{sec ( x )} + tan (x)