Is 2sin(y)cos(y)sec(2y)=tan(2y) ?

The answer to whether 2sin(y)cos(y)sec(2y)=tan(2y) is True

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prove 2sin(y)cos(y)sec(2y)=tan(2y)

prove

2 sin (y) cos (y) sec (2 y) = tan (2 y)

True

Solution steps

2 sin (y) cos (y) sec (2 y) = tan (2 y)

Manipulating left side

2 sin (y) cos (y) sec (2 y)

Rewrite using trig identities

2 sin (y) cos (y) sec (2 y)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 y) sec (2 y)

Express with sin, cos

sec (2 y) sin (2 y)

Use the basic trigonometric identity:

sec (2 y) = \frac{1}{cos ( 2 y )}

= \frac{1}{cos ( 2 y )} sin (2 y)

Simplify

\frac{1}{cos ( 2 y )} sin (2 y) : \frac{sin ( 2 y )}{cos ( 2 y )}

\frac{1}{cos ( 2 y )} sin (2 y)

Multiply fractions:

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

= \frac{1 sin ( 2 y )}{cos ( 2 y )}

Multiply:

1 \cdot sin (2 y) = sin (2 y)

= \frac{sin ( 2 y )}{cos ( 2 y )}

= \frac{sin ( 2 y )}{cos ( 2 y )}

= \frac{sin ( 2 y )}{cos ( 2 y )}

Use the basic trigonometric identity:

\frac{sin ( 2 y )}{cos ( 2 y )} = tan (2 y)

= tan (2 y)

= tan (2 y)

We showed that the two sides could take the same form

\Rightarrow True

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Is 2sin(y)cos(y)sec(2y)=tan(2y) ?
The answer to whether 2sin(y)cos(y)sec(2y)=tan(2y) is True