Is sin(x)+(cot(x))/(sec(x))=csc(x) ?

The answer to whether sin(x)+(cot(x))/(sec(x))=csc(x) is True

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prove sin(x)+(cot(x))/(sec(x))=csc(x)

prove

sin (x) + \frac{cot ( x )}{sec ( x )} = csc (x)

True

Solution steps

sin (x) + \frac{cot ( x )}{sec ( x )} = csc (x)

Manipulating left side

sin (x) + \frac{cot ( x )}{sec ( x )}

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

csc (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( 2 θ )}{sin ( θ )} = 2

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

- 2 sin (2 x + π) = - 2 sin (2 x - π)

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

2 sin (a + b) sin (a - b) = cos (2 b) - cos (2 a)

Is sin(x)+(cot(x))/(sec(x))=csc(x) ?
The answer to whether sin(x)+(cot(x))/(sec(x))=csc(x) is True