Question

If 3 cosec square (80degree-2x)=4.
Then the value of x is ??

Answer 1

$\huge\underline\mathfrak\red{ANSWER}$

$3 {cosec}^{2}( 80 - 2x) = 4 \\ \\ {cosec}^{2} (80 - 2x) = \frac{4}{3} \\ \\ cosec(80 - 2x) = \frac{2}{ \sqrt{3} } \: \: \ \\ : if \: we \: take \: positive \\ \\ sin(80 - 2x) = \frac{ \sqrt{3} }{2} \\ \\ we \: know \: that \: sin60 = \frac{ \sqrt{3} }{2} \\ \\ sin(80 - 2x) = sin60 \\ \\ by \: comparing \\ \\ 80 - 2x = 60 \\ \\ - 2x = - 20 \\ \\ x = 10 \\ \\ if \: we \: take \: negative \\ \\ cosec(8 0 - 2x) = \frac{ - 2}{ \sqrt{3} } \\ \\ sin(80 - 2x) = \frac{ - \sqrt{3} }{2} \\ \\ by \: comparing \: with \: sin( - 60) \\ \\ 80 - 2x = - 60 \\ \\ - 2x = - 140 \\ \\ x = 70 \\ \\ (1) \: solution \: of \: x = 10 \\ (2)solution \: of \: x \: = 70$

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