2 x = 1, then cos4 x + cos2 x is..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep."> 2 x = 1, then cos4 x + cos2 x is..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." /> 2 x = 1, then cos4 x + cos2 x is..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." />

Question 47

Mathematics Trigonometric Equations Hard

If sin x + sin<sup>2</sup>&nbsp;x = 1, then cos<sup>4</sup>&nbsp;x + cos<sup>2</sup>&nbsp;x is equal to:

(A) 0
(B) 1
(C) -1
(D) 2
✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\(\sin x + \sin^2 x = 1 \Rightarrow \sin x = 1 - \sin^2 x = \cos^2 x\)

Then \(\cos^4 x + \cos^2 x = (\cos^2 x)^2 + \cos^2 x = \sin^2 x + \sin x = 1\)

Answer: (B) 1

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