Question

if sin a = 1/2 prove that (3cos a-4cos^3 a)=0

Answer 1

Answer:

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Answer 2

Answer:

$lf\:sinA = \frac{1}{2}\:then\:3cosA-4cos^{3}A=0$

Step-by-step explanation:

$SinA = \frac{1}{2}\\=sin 30\degree$

$\implies A = 30\degree$

$Now, LHS = 3cosA-4cos^{3}A\\=3Cos30-4cos^{3}30\\=3\times \left(\frac{\sqrt{3}}{2}\right)-4\times \left(\frac{\sqrt{3}}{2}\right)^{3}\\=\frac{3\sqrt{3}}{2}-4\times \frac{3\sqrt{3}}{8}\\=\frac{3\sqrt{3}}{2}-\frac{3\sqrt{3}}{2}\\=0\\=RHS$

Therefore,

$lf\:sinA = \frac{1}{2}\:then\:3cosA-4cos^{3}A=0$

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