Is tan(θ)sin(θ)=sec(θ)-cos(θ) ?

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

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prove tan(θ)sin(θ)=sec(θ)-cos(θ)

prove

tan (θ) sin (θ) = sec (θ) - cos (θ)

True

Solution steps

tan (θ) sin (θ) = sec (θ) - cos (θ)

Manipulating left side

tan (θ) sin (θ)

Express with sin, cos

= \frac{sin ^{2} ( θ )}{cos ( θ )}

Rewrite using trig identities

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

Manipulating right side

sec (θ) - cos (θ)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ( θ )}{tan ( θ )} = csc (θ)

cot (2 b) = \frac{cot ^{2} ( b ) - 1}{2 cot ( b )}

1 + tan^{2} (a) = sec^{2} (a)

2 cos (x) cos (y) = cos (x + y) + cos (x - y)

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

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