Question

Determine the value of 'x' if 2 cosec square 30 degree +x.sin square 60 degree -tan square 30 degree =10
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Answer 1

Step-by-step explanation:

$2 cosec^{2} 30 + x \sin ^{2} 60 - { \tan}^{2} 30 = 10 \\ 2 \times {2}^{2} + x \times ( { \frac{ \sqrt{3} }{2} })^{2} - ( { \frac{1}{ \sqrt{3} } })^{2} = 10 \\ 8 + x \times \frac{3}{4} - \frac{1}{3} = 10 \\ 8 + \frac{3x}{4} - \frac{1}{3} = 10 \\ \frac{3x}{4} - \frac{1}{3} = 10 - 8 \\ \frac{3x}{4} - \frac{1}{3} = 2 \\ \frac{3x}{4} = 2 + \frac{1}{3} \\ \frac{3x}{4} = \frac{6 + 1}{3} \\ 3x = \frac{28}{3} \\ x = \frac{28}{9} \\ x = 3.11$