Is sec(θ)-cos(θ)=sin(θ)*tan(θ) ?

The answer to whether sec(θ)-cos(θ)=sin(θ)*tan(θ) is True

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prove sec(θ)-cos(θ)=sin(θ)*tan(θ)

prove

sec (θ) - cos (θ) = sin (θ) \cdot tan (θ)

True

Solution steps

sec (θ) - cos (θ) = sin (θ) tan (θ)

Manipulating left side

sec (θ) - cos (θ)

Express with sin, cos

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

Manipulating right side

sin (θ) tan (θ)

Express with sin, cos

= \frac{sin ^{2} ( θ )}{cos ( θ )}

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

(2 sin (x) + cos (x))^{2} + (2 cos (x) - sin (x))^{2} = 5

cos (a) (sec (a) - cos (a)) = sin^{2} (a)

tan (x) cos (x) csc (x) = 1

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

\frac{csc ^{4} ( x ) - 1}{1 + csc ^{2} ( x )} = cot^{2} (x)

Is sec(θ)-cos(θ)=sin(θ)*tan(θ) ?
The answer to whether sec(θ)-cos(θ)=sin(θ)*tan(θ) is True