Is sin^2(A)-sin^2(A)cos^2(A)=sin^4(A) ?

The answer to whether sin^2(A)-sin^2(A)cos^2(A)=sin^4(A) is True

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prove sin^2(A)-sin^2(A)cos^2(A)=sin^4(A)

prove

sin^{2} (A) - sin^{2} (A) cos^{2} (A) = sin^{4} (A)

True

Solution steps

sin^{2} (A) - sin^{2} (A) cos^{2} (A) = sin^{4} (A)

Manipulating left side

sin^{2} (A) - sin^{2} (A) cos^{2} (A)

Rewrite using trig identities

= sin^{4} (A)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sin ( x ) cos ( x )} = sec (x) csc (x)

cot^{2} (x) + csc^{2} (x) = 1 + 2 cot^{2} (x)

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

\frac{tan ( y ) + cot ( y )}{csc ( y )} = sec (y)

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

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