Is cos(x)tan^2(x)+cos(x)=sec(x) ?

The answer to whether cos(x)tan^2(x)+cos(x)=sec(x) is True

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prove cos(x)tan^2(x)+cos(x)=sec(x)

prove

cos (x) tan^{2} (x) + cos (x) = sec (x)

True

Solution steps

cos (x) tan^{2} (x) + cos (x) = sec (x)

Manipulating left side

cos (x) tan^{2} (x) + cos (x)

Express with sin, cos

= \frac{cos ^{2} ( x ) + sin ^{2} ( x )}{cos ( x )}

Rewrite using trig identities

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

Rewrite using trig identities

sec (x)

We showed that the two sides could take the same form

\Rightarrow True

1 - sin (x) = cos (x)

cos^{2} (x) csc (x) - csc (x) = - sin (x)

\frac{cos ( θ )}{sec ( θ ) - tan ( θ )} = 1 + sin (θ)

cot (- x) cos (- x) + sin (- x) = - csc (x)

cot (θ) + tan (θ) = csc (θ) sec (θ)

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