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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2023 · Mathematics · Trigonometric Ratios & Identities

If f(x)=x (4 x²-3) , then what is f( θ)equal to?

If f(x)=x(4x2−3)f(x)=x \left(4 x²-3\right), then what is f(sin⁡θ)equalto?f(\sin \theta)equal to?

Options

  1. A−sin⁡3θ-\sin 3 \theta
  2. B−cos⁡3θ-\cos 3 \theta
  3. Csin⁡3θ\sin 3 \theta
  4. D−sin⁡4θ-\sin 4 \theta

Correct answer

A. −sin⁡3θ-\sin 3 \theta

Step-by-step solution

f(x)=x(4x2−3)f(sin⁡θ)=sin⁡θ(4sin⁡2θ−3)=−(3sin⁡θ−4sin⁡3θ)=−sin⁡3θf(x)=x\left(4 x^2-3\right)f(\sin \theta)=\sin \theta\left(4 \sin ^2 \theta-3\right)=-\left(3 \sin \theta-4 \sin ^3 \theta\right)=-\sin 3 \theta
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