Question

3 cos theta + cos 3 theta divided by 3 sin theta minus sin 3 theta is equal to

Answer 1

Let theta =a
We have to find
(3 Cos a+cos 3a)/(3sina-sin3a)
=(3 cosa+4cos^3a-3cosa)/(3sina-3sina+4sin^3a)
=4cos^3a/4sin^3a
=tan^3a
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Answer 2

cot³theta is the correct answer.

Step-by-step explanation:

• we know that cos3θ=4cos³θ−3cosθ⟹cos3θ+3cosθ=4cos³θ -----(1)
• and sin3θ=3sinθ−4sin³θ⟹3sinθ−sin3θ=4sin³θ ------(2)
• Therefore,  3cosθ+cos3θ/3sinθ−sin3θ = 4cos³θ/ 4sin³θ

• (cosθ/sinθ)³ =cot³θ.
• Hence, cot³θ is the final answer.

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