Is 2sec(2α)cos(2α)=2 ?

The answer to whether 2sec(2α)cos(2α)=2 is True

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prove 2sec(2α)cos(2α)=2

prove

2 sec (2 α) cos (2 α) = 2

True

Solution steps

2 sec (2 α) cos (2 α) = 2

Manipulating left side

2 sec (2 α) cos (2 α)

Express with sin, cos

2 cos (2 α) sec (2 α)

Use the basic trigonometric identity:

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

= 2 cos (2 α) \frac{1}{cos ( 2 α )}

2 cos (2 α) \frac{1}{cos ( 2 α )} = 2

2 cos (2 α) \frac{1}{cos ( 2 α )}

Multiply fractions:

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

= \frac{1 \cdot 2 cos ( 2 α )}{cos ( 2 α )}

Cancel the common factor:

cos (2 α)

= 1 \cdot 2

Multiply the numbers:

1 \cdot 2 = 2

= 2

= 2

= 2

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sec ( x )} + 1 = \frac{sec ( x ) + 1}{sec ( x )}

tan^{2} (θ) = sec (θ) csc (θ) tan (θ) - 1

sin (x + y) = cos (\frac{π}{2} - (x + y))

(sin (x) + cos (x))^{2} = 1 + 2 cos (x)

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