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

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

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prove sin(y)sec(y)=tan(y)

prove

sin (y) sec (y) = tan (y)

True

Solution steps

sin (y) sec (y) = tan (y)

Manipulating left side

sin (y) sec (y)

Express with sin, cos

sec (y) sin (y)

Use the basic trigonometric identity:

sec (y) = \frac{1}{cos ( y )}

= \frac{1}{cos ( y )} sin (y)

Simplify

\frac{1}{cos ( y )} sin (y) : \frac{sin ( y )}{cos ( y )}

\frac{1}{cos ( y )} sin (y)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 sin ( y )}{cos ( y )}

Multiply:

1 \cdot sin (y) = sin (y)

= \frac{sin ( y )}{cos ( y )}

= \frac{sin ( y )}{cos ( y )}

= \frac{sin ( y )}{cos ( y )}

Use the basic trigonometric identity:

\frac{sin ( y )}{cos ( y )} = tan (y)

= tan (y)

We showed that the two sides could take the same form

\Rightarrow True

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