Is 2+sec(a)cos(a)=3 ?

The answer to whether 2+sec(a)cos(a)=3 is True

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prove 2+sec(a)cos(a)=3

prove

2 + sec (a) cos (a) = 3

True

Solution steps

2 + sec (a) cos (a) = 3

Manipulating left side

2 + sec (a) cos (a)

Express with sin, cos

2 + cos (a) sec (a)

Use the basic trigonometric identity:

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

= 2 + cos (a) \frac{1}{cos ( a )}

2 + cos (a) \frac{1}{cos ( a )} = 3

2 + cos (a) \frac{1}{cos ( a )}

cos (a) \frac{1}{cos ( a )} = 1

cos (a) \frac{1}{cos ( a )}

Multiply fractions:

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

= \frac{1 \cdot cos ( a )}{cos ( a )}

Cancel the common factor:

cos (a)

= 1

= 2 + 1

Simplify

= 3

= 3

= 3

We showed that the two sides could take the same form

\Rightarrow True

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