Is (cot^2(x)-1)/(csc(x)+1)=csc(x)-1 ?

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

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prove (cot^2(x)-1)/(csc(x)+1)=csc(x)-1

prove

\frac{cot ^{2} ( x ) - 1}{csc ( x ) + 1} = csc (x) - 1

False

Solution steps

\frac{cot ^{2} ( x ) - 1}{csc ( x ) + 1} = csc (x) - 1

Show that the two sides are not equal

For

\frac{cot ^{2} ( x ) - 1}{csc ( x ) + 1} = csc (x) - 1

plug in

x = 1

\frac{cot ^{2} ( 1 ) - 1}{csc ( 1 ) + 1} = - 0.26856 \dots

\frac{cot ^{2} ( 1 ) - 1}{csc ( 1 ) + 1}

Refine to a decimal form

= - 0.26856 \dots

csc (1) - 1 = 0.18839 \dots

csc (1) - 1

Refine to a decimal form

= 0.18839 \dots

The two sides are not equal

\Rightarrow False

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

\frac{( cos ( π + x ) )}{cos ( \frac{3 π}{2} - x )} = cot (x)

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

tan (A + π) = tan (A)

sin (12 0^{\circ}) = sin (18 0^{\circ} - 6 0^{\circ})

Is (cot^2(x)-1)/(csc(x)+1)=csc(x)-1 ?
The answer to whether (cot^2(x)-1)/(csc(x)+1)=csc(x)-1 is False