Question

cos⁻¹(cos7π/6)=..........,Select Proper option from the given options.
(a) π/6
(b) 5π/6
(c) - π/6
(d) 7π/6

Answer 1

Answer:

option (b) is correct

Step-by-step explanation:

$cos^{-1}(cos\frac{7\pi}{6})$

$\boxed{\begin{minipage}{2cm} \bf\:cos\frac{7\pi}{6}\\ \\=cos(\pi+\frac{\pi}{6})\\ \\=-cos\frac{\pi}{6}\\ \\=-\frac{\sqrt3}{2} \end{minipage}}$

$=cos^{-1}(\frac{-\sqrt3}{2})$

Using

$\boxed{cos^{-1}(-x)=\pi-cos^{1}x}$

$=\pi-cos^{-1}(\frac{\sqrt3}{2})$

$=\pi-\frac{\pi}{6}$

$=\frac{6\:\pi-\pi}{6}$

$=\frac{5\pi}{6}$

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$\sf{If \: \: \alpha \: \: is \: the \: principal \: value \: of \: \: { \cos}^{ - 1}x \: \: then}$

$\sf{ \:0 \leqslant \alpha \leqslant \pi \: }$

TO DETERMINE

$\displaystyle \sf{ { \cos}^{ - 1} ( \cos \frac{7\pi}{6} )\: \: }$

CALCULATION

$\displaystyle \sf{ { \cos}^{ - 1} \bigg( \cos \frac{7\pi}{6} \bigg)\: \: }$

$= \displaystyle \sf{ { \cos}^{ - 1} \bigg( \cos (\pi + \frac{ \pi}{6} ) \bigg)\: \: }$

$= \displaystyle \sf{ { \cos}^{ - 1} \bigg( - \cos \frac{ \pi}{6} \bigg)\: \: }$

$= \displaystyle \sf{ { \cos}^{ - 1} \bigg( \cos (\pi - \frac{ \pi}{6} ) \bigg)\: \: }$

$= \displaystyle \sf{ { \cos}^{ - 1} \bigg( \cos \frac{ 5\pi}{6} \bigg)\: \: }$

$= \displaystyle \sf{ \frac{ 5\pi}{6} \: } \: \: \: \: (\because \: 0 \leqslant\frac{ 5\pi}{6} \leqslant \pi \: \: \: )$

RESULT

$\boxed{\displaystyle \sf{ \: \: \: \: { \cos}^{ - 1} \bigg( \cos \frac{7\pi}{6} \bigg)\: = \frac{5\pi}{6} \: \: \: \: }}$

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LEARN MORE FROM BRAINLY

tan⁻¹(x/y)-tan⁻¹(x-y/x+y)=

Select Proper option from the given options.

(a) π/4 (b) π/3 (c) π/2 (d) π

https://brainly.in/question/5596504