Question

Prove that
4(cos³10°+sin³20°) = 3(cos10°+sin20°)​

Answer 1

Step-by-step explanation:

cos 3θ = 4cos^3 θ - 3cosθ

=> 4cos^3 θ = cos3θ + 3 cosθ

Taking θ = 10°

=> 4cos^3 10° = cos30° + 3cos10° ... ( 1 )

sin3θ = 3sinθ - 4sin^3 θ

=> 4sin^3 θ = 3sinθ - sin3θ

Taking θ = 20°

=> 4sin^3 20° = 3sin20° - sin60° ... ( 2 )

Adding ( 1 ) and ( 2 ),

4(cos^3 10° + sin^3 20°) = 3(cos10° + sin20°) + cos30° - sin60°

=> 4(cos^3 10° + sin^3 20°) = 3(cos10° + sin20°) ... [because cos30° = sin60°]

Edit:

I always appreciate thumbs down as they draw attention to the possible error. In the above solution, I have repeatedly rechecked the steps and found no error. I shall be grateful if someone points out the error in my above solution.

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