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

The answer to whether prove-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)

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

\frac{sin ( 3 x )}{sin ( 2 x )} = 2 cos (x) - \frac{1}{2} sec (x)

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

cos (1 5^{\circ}) = cos (4 5^{\circ} - 3 0^{\circ})

1 - csc^{2} (x) = - cot^{2} (x)

sec (x) + sec^{2} (x) = 2

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