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} = 0.45695 \dots

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

Refine to a decimal form

= 0.45695 \dots

\frac{1}{sin ( 1 ) + 1} = 0.54304 \dots

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

Refine to a decimal form

= 0.54304 \dots

The two sides are not equal

\Rightarrow False

tan (θ) + 1 = \frac{sin ( θ )}{cos ( θ )} + 1

(1 + tan^{2} (α)) cos^{2} (α) = 1

\frac{1}{sin ^{2} ( x )} = \frac{1}{csc ^{2} ( x )}

sin^{2} (θ) = (1 - cos^{2} (θ))

sin (x) (1 + tan^{2} (x)) = sin (x) sec^{2} (x)

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