Question : If $\sin A+\sin ^2 A=1$, then the value of $\cos ^4 A+\cos ^6 A$ is:
Option 1: $\cos A$
Option 2: $\sin A$
Option 3: 1
Option 4: 0
Correct Answer: $\sin A$
Solution : Given: $\sin A+\sin ^2 A=1$ ⇒ $\sin A=1-\sin ^2 A$ ⇒ $\sin A=\cos ^2 A$ ⇒ $\sin^2 A=\cos ^4 A$ Now, $\cos ^4 A+\cos ^6 A$ = $\cos^2 A(\cos ^2 A+\cos ^4 A)$ Putting the values, we get: = $\sin A(\sin A+\sin^2 A)$ Since, $\sin A+\sin ^2 A=1$ = $\sin A\times 1$ = $\sin A$ Hence, the correct answer is $\sin A$.
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