Question

If cos
(40+x)° = sin 30° find the valueof x
​

Answer 1

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Step-by-step explanation:

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Answer 2

$\begin{gathered}\begin{gathered}\bf \: Given - \begin{cases} &\sf{cos(40 + x)\degree \: = sin30\degree \:} \\ \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\:find - \begin{cases} &\sf{the \: value \: of \: x} \\   \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}}  \end{gathered}$

$\boxed{ \bf{sin(90\degree \: - x) = cosx}}$

$\large\underline{\sf{Solution-}}$

Given that,

$\rm :\longmapsto\:cos(40 + x)\degree \: = sin30\degree \:$

$\rm :\longmapsto\:cos(40 + x)\degree \: = sin(90\degree \: - 60\degree)$

$\rm :\longmapsto\:cos(40 + x)\degree \: = cos60\degree \:$

So, on comparing, we get

$\rm :\longmapsto\:40 + x = 60$

$\bf\implies \:x \: = \: 20$

Additional Information :-

$1. \: \: \boxed{ \bf{sin(90\degree \: - x) = cosx}}$

$2. \: \: \boxed{ \bf{cos(90\degree \: - x) = sinx}}$

$3. \: \: \boxed{ \bf{tan(90\degree \: - x) = cotx}}$

$4. \: \: \boxed{ \bf{cot(90\degree \: - x) = tanx}}$

$5. \: \: \boxed{ \bf{sec(90\degree \: - x) = cosecx}}$

$6. \: \: \boxed{ \bf{cosec(90\degree \: - x) = secx}}$