Is (sin^4(x)-1)/(cos^2(x))=cos^2(x)-2 ?

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

Popular >

prove (sin^4(x)-1)/(cos^2(x))=cos^2(x)-2

prove

\frac{sin ^{4} ( x ) - 1}{cos ^{2} ( x )} = cos^{2} (x) - 2

True

Solution steps

\frac{sin ^{4} ( x ) - 1}{cos ^{2} ( x )} = cos^{2} (x) - 2

Manipulating left side

\frac{sin ^{4} ( x ) - 1}{cos ^{2} ( x )}

Rewrite using trig identities

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

Manipulating right side

cos^{2} (x) - 2

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

tan^{2} (A) - sin^{2} (A) = tan^{2} (A) sin^{2} (A)

cos (θ) sec (\frac{π}{2} - θ) = cot (θ)

csc (x) (1 + sin (x)) = 1 + csc (x)

sin (x + y) sin (x - y) = sin (2 x) - sin (2 y)

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