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) sin (x) = tan (x)

True

Solution steps

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

Manipulating left side

sec (- x) sin (x)

Use the negative angle identity:

sec (- x) = sec (x)

= sec (x) sin (x)

Rewrite using trig identities

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)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e \frac{cos ^{2} ( v )}{sin ( v )} = csc (v) - sin (v)

p ro v e sin (2 x) = 2 cot (x) sin^{2} (x)

p ro v e \frac{sec ( t ) - cos ( t )}{sec ( t )} = sin^{2} (t)

p ro v e \frac{1}{tan ( x )} + tan (x) = sec (x) csc (x)

p ro v e tan (θ) + cot (θ) = 2 csc (2 θ)