Cos90=4cos³30–3cos30, Verify It.
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Solve this as shown in the attachment.
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cos90° = 0
4cos³30° - 3cos30°
we know, cos30° = √3/2
so, 4cos³30° - 3cos30° = 4{√3/2}³ - 3{√3/2}
= 4 × {√3/2 × √3/2 × √3/2} - 3√3/2
= 4 × 3√3/8 - 3√3/2
= 3√3/2 - 3√3/2
= 0
here it is clear that cos90° = 4cos³30°-3cos30°
hence, verified
4cos³30° - 3cos30°
we know, cos30° = √3/2
so, 4cos³30° - 3cos30° = 4{√3/2}³ - 3{√3/2}
= 4 × {√3/2 × √3/2 × √3/2} - 3√3/2
= 4 × 3√3/8 - 3√3/2
= 3√3/2 - 3√3/2
= 0
here it is clear that cos90° = 4cos³30°-3cos30°
hence, verified
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