Is 1/(csc(x))+1= 1/(sin(x))+1 ?

The answer to whether 1/(csc(x))+1= 1/(sin(x))+1 is False

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prove 1/(csc(x))+1= 1/(sin(x))+1

prove

\frac{1}{csc ( x )} + 1 = \frac{1}{sin ( x )} + 1

False

Solution steps

\frac{1}{csc ( x )} + 1 = \frac{1}{sin ( x )} + 1

Show that the two sides are not equal

For

\frac{1}{csc ( x )} + 1 = \frac{1}{sin ( x )} + 1

plug in

x = 1

\frac{1}{csc ( 1 )} + 1 = 1.84147 \dots

\frac{1}{csc ( 1 )} + 1

Refine to a decimal form

= 1.84147 \dots

\frac{1}{sin ( 1 )} + 1 = 2.18839 \dots

\frac{1}{sin ( 1 )} + 1

Refine to a decimal form

= 2.18839 \dots

The two sides are not equal

\Rightarrow False

(sin (2 θ)) (tan (θ)) + cos (2 θ) = 1

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

cot^{2} (θ) = \frac{csc ^{2} ( θ )}{sec ^{2} ( θ )}

\frac{1}{sec ( θ )} = arcsec (θ)

\frac{( cot ( x ) )}{( csc ( x ) )} = cos (x)

Is 1/(csc(x))+1= 1/(sin(x))+1 ?
The answer to whether 1/(csc(x))+1= 1/(sin(x))+1 is False