Find the value of each power. 7:4 and (3/4)^3

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7obadiah

06.06.2020

We have the following difference identities for sine and cosine: $\begin{aligned} \sin(a-b) & = \sin a\cos b - \cos a\sin b \\ \cos(a-b) & = \cos a \cos b + \sin a \sin b \end{aligned}$ also, $\sin(90^{\circ}) = 1$ and $\cos(90^{\circ}) = 0$ ===if $\tan x = \dfrac{\sin x}{\cos x}$ then $\tan(90^{\circ} - a) = \dfrac{\sin(90^{\circ} - a)}{\cos (90^{\circ} - a)}$ using the difference formulas $\dfrac{\sin(90^{\circ} - a)}{\cos (90^{\circ} - a)} \\ \begin{aligned} & =\dfrac{\sin(90^{\circ})\cos a - \cos(90^{\circ})\sin a}{\cos(90^{\circ})\cos a + \sin(90^{\circ}) \sin a} \\ & =\dfrac{(1)\cos a - (0)\sin a}{(0)\cos a + (1) \sin a} \\ & =\dfrac{\cos a}{\sin a} \\ & = \cot a \end{aligned}$ therefore, $\tan(90^{\circ} - a) = \cot a$

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Find the value of each power. 7:4 and (3/4)^3

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