Is (sin(θ)+1)(sin(θ)-1)=-cos^2(θ) ?

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

Popular >

prove (sin(θ)+1)(sin(θ)-1)=-cos^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

(sin (θ) + 1) (sin (θ) - 1)

Expand

(sin (θ) + 1) (sin (θ) - 1) : sin^{2} (θ) - 1

= sin^{2} (θ) - 1

Use the Pythagorean identity:

1 = cos^{2} (θ) + sin^{2} (θ)

1 - sin^{2} (θ) = cos^{2} (θ)

= - cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (x) = sin (x)

csc (x) - cot (x) = tan (\frac{x}{2})

cot^{2} (a) - cos^{2} (a) = cot^{2} (a) cos^{2} (a)

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

cos^{2} (θ) (sec^{2} (θ) - 1) = sin^{2} (θ)

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