Is sec(x)csc(x)-cot(x)=tan(x) ?

The answer to whether sec(x)csc(x)-cot(x)=tan(x) is True

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prove sec(x)csc(x)-cot(x)=tan(x)

prove

sec (x) csc (x) - cot (x) = tan (x)

True

Solution steps

sec (x) csc (x) - cot (x) = tan (x)

Manipulating left side

sec (x) csc (x) - cot (x)

Express with sin, cos

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

Rewrite using trig identities

= \frac{sin ( x )}{cos ( x )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) sin (2 θ) = 2 - 2 cos^{2} (θ)

- 30 cos (3 x) sin (3 x) = - 15 sin (6 x)

2 sin^{2} (θ) - 1 = sin^{4} (θ) - cos^{4} (θ)

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

csc^{4} (θ) - cot^{4} (θ) = 2 cot^{2} (θ) + 1

Is sec(x)csc(x)-cot(x)=tan(x) ?
The answer to whether sec(x)csc(x)-cot(x)=tan(x) is True