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Quantitative Aptitude (CGL)

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What is the value of sin (90° + 2A)[4 - cos²(90° - 2A)]?

2(cos³A - sin³A)

2(cos³A + sin³A)

4(cos⁶A + sin⁶A)

4(cos⁶A - sin⁶A)

Explanation:

We have, sin(90° + A) = cosA and cos(90° - A) = sinA
Applying the above formulas, the expression becomes,
⇒ cos2A × (4 - sin²2A)
Also, sin2A = 2sinA.cosB
⇒ cos2A × (4 - 4sin²A.cos²A) = 4 × cos²A × (1 - sin²A.cos²A)
Substituting (sin2A + cos2A)² instead of 1, we get
⇒ 4 × cos2A × [(sin²A + cos²A)2 - sin²A.cos²A]
⇒ 4 × cos2A × (sin⁴A + cos⁴A + sin²A.cos²A)
⇒ 4 × (cos²A - sin²A) × [sin⁴A + cos⁴A + sin²A.cos²A] = 4 (cos⁶A - sin⁶A)

By: MIRZA SADDAM HUSSAIN

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