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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(sin (x) + 1) (sin (x) - 1)

Expand

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

= sin^{2} (x) - 1

Use the Pythagorean identity:

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

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

= - cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sec (\frac{3 π}{2} - x) = - csc (x)

\frac{( sec ^{2} ( x ) - 1 )}{sec ^{2} ( x )} = sin^{2} (x)

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

cos (α + β) - cos (α - β) = - 2 sin (α) sin (β)

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