Question

$2sin {}^{2} 30 + cosec {}^{2} 210 \: cos {}^{2} 60$


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Answer 1

Answer:

3/2 = 1.5

Step-by-step explanation:

$To \ find \ : 2sin^{2}30 +cosec^{2}210 \ cos^{2}60 \\\\ => sin 30 = \frac{1}{2} \\\\=> cos 60=\frac{1}{2} \\\\=> cosec 210 = cosec(270-60) =-sec60 = -[\frac{1}{cos60} ] = \frac{-1}{\frac{1}{2}} = -2 \\\\\\\\=>2sin^{2}30 +cosec^{2}210 \ cos^{2}60 \\\\=>2(\frac{1}{2} )^{2}+(-2)^{2} \ (\frac{1}{2} )^{2} \\\\=>2(\frac{1}{4} )+4(\frac{1}{4} )\\\\=>\frac{1}{2} +1 \\\\=> \frac{3}{2}$