Is ((cos^2(x)+4cos(x)+4))/((cos(x)+2))=((2sec(x)+1))/(sec(x)) ?

The answer to whether ((cos^2(x)+4cos(x)+4))/((cos(x)+2))=((2sec(x)+1))/(sec(x)) is True

Popular >

prove ((cos^2(x)+4cos(x)+4))/((cos(x)+2))=((2sec(x)+1))/(sec(x))

prove

\frac{( cos ^{2} ( x ) + 4 cos ( x ) + 4 )}{( cos ( x ) + 2 )} = \frac{( 2 sec ( x ) + 1 )}{sec ( x )}

True

Solution steps

\frac{cos ^{2} ( x ) + 4 cos ( x ) + 4}{cos ( x ) + 2} = \frac{2 sec ( x ) + 1}{sec ( x )}

Manipulating left side

\frac{cos ^{2} ( x ) + 4 cos ( x ) + 4}{cos ( x ) + 2}

Simplify

\frac{4 + cos ^{2} ( x ) + 4 cos ( x )}{2 + cos ( x )} : cos (x) + 2

= 2 + cos (x)

Manipulating right side

\frac{2 sec ( x ) + 1}{sec ( x )}

Express with sin, cos

= 2 + cos (x)

We showed that the two sides could take the same form

\Rightarrow True

5 cos^{2} (x) - 5 sin^{2} (x) = 10 cos^{2} (x) - 5

sin (a) tan (a) + cos (a) = sec (a)

sin (x) (sec (x) - csc (x)) = tan (x) - 1

tan (x) = \frac{( 1 - cos ( 2 x ) )}{( sin ( 2 x ) )}

sec^{2} (x) csc^{2} (x) = csc^{2} (x) + sec^{2} (x)

Is ((cos^2(x)+4cos(x)+4))/((cos(x)+2))=((2sec(x)+1))/(sec(x)) ?
The answer to whether ((cos^2(x)+4cos(x)+4))/((cos(x)+2))=((2sec(x)+1))/(sec(x)) is True