If cosx + cos2x = 1, the value of sin12x

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Target Exam

CUET

Subject

General Aptitude Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If cosx + cos²x = 1, the value of sin¹²x + 3sin⁸x + sin⁶x - 1 is:

Options:

sin¹²x + sin⁶x

Correct Answer:

Explanation:

cosx + cos²x = 1

⇒ cosx = 1 - cos²x

⇒ cosx = sin²x

∴ sin¹²x + 3sin¹⁰x + 3sin⁸x + sin⁶x - 1

= ( sin⁴x + sin²x)³ - 1

= (cos²x + sin²x) - 1

= 1 - 1 = 0