Is sec(a)-cos(a)=sin(a)tan(a) ?

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

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prove sec(a)-cos(a)=sin(a)tan(a)

prove

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

True

Solution steps

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

Manipulating left side

sec (a) - cos (a)

Express with sin, cos

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

Manipulating right side

sin (a) tan (a)

Express with sin, cos

= \frac{sin ^{2} ( a )}{cos ( a )}

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

(sec (x) + tan (x)) (1 - sin (x)) = cos (x)

sin^{7} (x) = (1 - cos^{2} (x))^{3} sin (x)

tan (A) + cot (A) = sec (A) csc (A)

\frac{sec ( θ )}{csc ( θ )} = tan (θ)

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

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