Is tan(θ)=sin(θ)sec(θ) ?

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

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prove tan(θ)=sin(θ)sec(θ)

prove

tan (θ) = sin (θ) sec (θ)

True

Solution steps

tan (θ) = sin (θ) sec (θ)

Manipulating right side

sin (θ) sec (θ)

Express with sin, cos

sec (θ) sin (θ)

Use the basic trigonometric identity:

sec (θ) = \frac{1}{cos ( θ )}

= \frac{1}{cos ( θ )} sin (θ)

Simplify

\frac{1}{cos ( θ )} sin (θ) : \frac{sin ( θ )}{cos ( θ )}

\frac{1}{cos ( θ )} sin (θ)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 sin ( θ )}{cos ( θ )}

Multiply:

1 \cdot sin (θ) = sin (θ)

= \frac{sin ( θ )}{cos ( θ )}

= \frac{sin ( θ )}{cos ( θ )}

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

\frac{sin ( θ )}{cos ( θ )} = tan (θ)

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

sin (4 a) = 2 sin (2 a) cos (2 a)

tan (x) = sec (x) sin (x)

sin (2 D) = 2 cot (D) sin^{2} (D)