Is sec(x)*sin(x)=tan(x) ?

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

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prove sec(x)*sin(x)=tan(x)

prove

sec (x) \cdot sin (x) = tan (x)

True

Solution steps

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

Manipulating left side

sec (x) sin (x)

Express with sin, cos

sec (x) sin (x)

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot sin (x) = sin (x)

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

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

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

(1 - cos (θ)) (1 + sec (θ)) = sec (θ) - cos (θ)

tan (x) csc (x) sec (x) = tan^{2} (x) + 1

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

sin (2 x) cot (x) = 2 - 2 sin^{2} (x)

tan^{2} (x) csc^{2} (x) cot^{2} (x) sin^{2} (x) = 1