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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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)

We showed that the two sides could take the same form

\Rightarrow True

cot (B) sin (B) = cos (B)

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

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

2 csc (2 x) = csc^{2} (x) tan (x)

\frac{sec ^{2} ( t )}{tan ( t )} = cot (t) + tan (t)