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

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

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

prove

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

True

Solution steps

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

Manipulating right 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

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

tan^{2} (\frac{π}{6}) = \frac{1}{3}

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

(sin (a) + cos (a))^{2} - 2 sin (a) cos (a) = 1

cos (x) + sin (x) + tan (x) = sec (x)