Is tan(x)-1/(tan(x))=2sin^2(x)-1 ?

The answer to whether tan(x)-1/(tan(x))=2sin^2(x)-1 is False

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prove tan(x)-1/(tan(x))=2sin^2(x)-1

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

tan (1) - \frac{1}{tan ( 1 )} = 0.91531 \dots

tan (1) - \frac{1}{tan ( 1 )}

Refine to a decimal form

= 0.91531 \dots

2 sin^{2} (1) - 1 = 0.41614 \dots

2 sin^{2} (1) - 1

Refine to a decimal form

= 0.41614 \dots

The two sides are not equal

\Rightarrow False

\frac{1}{cot ( u )} = \frac{cot ( u )}{1}

sin^{2} (x) \cdot sec (x) = tan^{2} (x)

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

sin (2 x) = 2 cos (x)

sec (β) sin (β) cot (β) = 1

Is tan(x)-1/(tan(x))=2sin^2(x)-1 ?
The answer to whether tan(x)-1/(tan(x))=2sin^2(x)-1 is False