Question : If for any acute angle A, $\sin A+\sin^{2} A=1$, then the value of $\cos^{2}A+\cos^{4}A$ is:
Option 1: –1
Option 2: 1
Option 3: 2
Option 4: 0
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Correct Answer: 1
Solution :
Given: $\sin A+\sin^{2} A=1$ ----(1)
⇒ $\sin A=1–\sin^{2} A$
⇒ $\sin A=\cos^{2} A$ -----(2)
⇒ $\sin^{2} A=\cos^{4} A$ -----(3)
From equation (2) and (3), we get:
So, $\cos^{2} A+\cos^{4} A=\sin A+\sin^{2} A$
⇒ $\cos^{2} A+\cos^{4} A=1$
Hence, the correct answer is 1.
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