Is prove-sin(x)sec(x)=-tan(x) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

- sin (x) sec (x)

Rewrite using trig identities

- sin (x) sec (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

cos (4 x) - cos (3 x) cos (x) = sin (2 x) - 4 cos (2 x) sin (2 x)

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

cos (4 x) = 1 - 8 sin^{2} (x) cos (x)

\frac{( 1 )}{( 2 )} (cot (θ) - tan (θ)) = cot (2 θ)

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

Is prove-sin(x)sec(x)=-tan(x) ?
The answer to whether prove-sin(x)sec(x)=-tan(x) is True