Is sec(x)=(1+csc(x))/(cot(x)+cos(x)) ?

The answer to whether sec(x)=(1+csc(x))/(cot(x)+cos(x)) is True

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prove sec(x)=(1+csc(x))/(cot(x)+cos(x))

prove

sec (x) = \frac{1 + csc ( x )}{cot ( x ) + cos ( x )}

True

Solution steps

sec (x) = \frac{1 + csc ( x )}{cot ( x ) + cos ( x )}

Manipulating right side

\frac{1 + csc ( x )}{cot ( x ) + cos ( x )}

Express with sin, cos

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

Rewrite using trig identities

sec (x)

We showed that the two sides could take the same form

\Rightarrow True

9 sec^{2} (θ) - 5 tan^{2} (θ) = 5 + 4 sec^{2} (θ)

cot (2 θ) = cot (θ) - \frac{1}{2} sec (θ) csc (θ)

(csc (x) - cot (x)) (csc (x) + cot (x)) = 1

(tan (x)) (sin (x)) = sec (x) - cos (x)

tan (α) + cot (α) = sec (α) csc (α)

Is sec(x)=(1+csc(x))/(cot(x)+cos(x)) ?
The answer to whether sec(x)=(1+csc(x))/(cot(x)+cos(x)) is True