Is cos^2(x)+cos(x)-1+sin^2(x)=cos(x) ?

The answer to whether cos^2(x)+cos(x)-1+sin^2(x)=cos(x) is True

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prove cos^2(x)+cos(x)-1+sin^2(x)=cos(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

= - 1 + cos (x) + 1

Simplify

- 1 + cos (x) + 1 : cos (x)

- 1 + cos (x) + 1

Group like terms

= cos (x) - 1 + 1

- 1 + 1 = 0

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (x - \frac{3 π}{2}) = - cot (x)

tan (\frac{1}{2} x) + cos (\frac{1}{2} x) = 2 csc (x)

sin (θ) \frac{cos ^{2} ( θ )}{sin ( θ )} = csc (θ)

\frac{tan ^{2} ( a ) + 1}{sec ( a )} = sec (a)

Is cos^2(x)+cos(x)-1+sin^2(x)=cos(x) ?
The answer to whether cos^2(x)+cos(x)-1+sin^2(x)=cos(x) is True