Multiple choice

What is the value of [sin (90° - 10θ) - cos (180° - 6θ)]/[cos (90° - 10θ) - sin (180° - 6θ)]?

  1. tan 2θ

  2. cot 2θ

  3. cot θ

  4. cot 3θ
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B Correct answer
AI explanation

Use the co-function and quadrant trigonometric identities to simplify the expression. The numerator becomes cos 10 theta minus the negative of cos 6 theta, which equals cos 10 theta plus cos 6 theta. The denominator becomes sin 10 theta minus sin 6 theta. Using the sum-to-product identities, the numerator simplifies to 2 cos 8 theta cos 2 theta and the denominator simplifies to 2 cos 8 theta sin 2 theta. Canceling the common term of 2 cos 8 theta leaves cos 2 theta divided by sin 2 theta, which is cot 2 theta.

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