Question

What is the formula of cos³t

Answer 1

$\textbf{To find:}$

$\text{Formula of cos^3t }$

$\textbf{Solution:}$

$\text{We have following 3 multiple angle formulae in trigonometry}$

$\bf\,sin3A=3\,sinA-4\,sin^3A$

$\bf\,cos3A=4\,cos^3A-3\,cosA$

$\bf\,tan3A=\dfrac{3\,tanA-tan^3A}{1-3\,tan^2A}$

$\text{From these formulae, we get}$

$cos3t=4\,cos^3t-3\,cost$

$\implies\,4\,cos^3t=3\,cost+cos\,3t$

$\implies\bf\,cos^3t=\dfrac{3\,cost+cos\,3t}{4}$

$\therefore\boxed{\bf\,cos^3t=\dfrac{3\,cost+cos\,3t}{4}}$

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