Question

8) Using tables evaluate the following:
i) 4cot45º - sec 60° + sin 30°
$4 \cot(45) - \sec(60) + \sin(30)$
​

Answer 1

$\textbf{Given:}$

$\mathsf{4\,cot45^\circ-sec60^\circ+sin30^\circ}$

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{4\,cot45^\circ-sec60^\circ+sin30^\circ}$

$\textbf{Solution:}$

$\textbf{Standard trigonometric table:}$

$\left\begin{array}{|c|c|c|c|c|c|}\cline{1-6}&0^{\circ}&30^{\circ}&45^{\circ}&60^{\circ}&90^{\circ}\\\cline{1-6}\bf\,sin\theta&0&\frac{1}{2}&\frac{1}{\sqrt2}&\frac{\sqrt3}{2}&1\\\cline{1-6}\bf\,cos\theta&1&\frac{\sqrt3}{2}&\frac{1}{\sqrt2}&\frac{1}{2}&0\\\cline{1-6}\bf\,tan\theta&0&\frac{1}{\sqrt3}&1&\sqrt3&\infty\\\cline{1-6}\end{array}\right$

$\textsf{Consider,}$

$\mathsf{4\,cot45^\circ-sec60^\circ+sin30^\circ}$

$\mathsf{=4\left(\dfrac{1}{tan45^\circ}\right)-\dfrac{1}{cos60^\circ}+sin30^\circ}$

$\mathsf{=4\left(\dfrac{1}{1}\right)-\dfrac{1}{\dfrac{1}{2}}+\dfrac{1}{2}}$

$\mathsf{=4(1)-2+\dfrac{1}{2}}$

$\mathsf{=4-2+\dfrac{1}{2}}$

$\mathsf{=2+\dfrac{1}{2}}$

$\mathsf{=\dfrac{4+1}{2}}$

$\mathsf{=\dfrac{5}{2}}$

$\implies\boxed{\mathsf{4\,cot45^\circ-sec60^\circ+sin30^\circ=\dfrac{5}{2}}}$

$\textbf{Find more:}$

Evaluate sin 30 degree by cos 45 degree + cot 45 degree by sec 60 degree minus sin 60 degree by tan 45 degree minus cos 60 degree by sin 90 degree

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