prove 1/cos 290 degree  +  1/sq. root 3*sin 250 degree  = 4/sq. root 3

Asked by dev.sultanpur123 | 26th May, 2015, 11:39: AM

Expert Answer:

fraction numerator 1 over denominator cos 290 to the power of o end fraction plus fraction numerator 1 over denominator square root of 3 sin 250 to the power of o end fraction equals fraction numerator 1 over denominator cos open parentheses 360 to the power of o minus 70 to the power of o close parentheses end fraction plus fraction numerator 1 over denominator square root of 3 sin open parentheses 180 to the power of o plus 70 to the power of o close parentheses end fraction equals fraction numerator 1 over denominator cos 70 to the power of o end fraction minus fraction numerator 1 over denominator square root of 3 sin 70 to the power of o end fraction equals fraction numerator square root of 3 sin 70 to the power of o minus cos 70 to the power of o over denominator square root of 3 cos 70 to the power of o sin 70 to the power of o end fraction equals fraction numerator 2 open parentheses begin display style fraction numerator square root of 3 over denominator 2 end fraction end style sin 70 to the power of o minus begin display style 1 half end style cos 70 to the power of o close parentheses over denominator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style cross times 2 cos 70 to the power of o sin 70 to the power of o end fraction equals fraction numerator 2 open parentheses cos 30 to the power of o sin 70 to the power of o minus sin 30 to the power of o cos 70 to the power of o close parentheses over denominator fraction numerator square root of 3 over denominator 2 end fraction cross times sin 140 to the power of o end fraction equals fraction numerator 2 sin open parentheses 70 to the power of o minus 30 to the power of o close parentheses over denominator fraction numerator square root of 3 over denominator 2 end fraction cross times sin 140 to the power of o end fraction equals fraction numerator 2 sin 40 to the power of o over denominator fraction numerator square root of 3 over denominator 2 end fraction cross times sin 140 to the power of o end fraction equals fraction numerator 4 over denominator square root of 3 end fraction cross times fraction numerator sin open parentheses 180 to the power of o minus 140 to the power of o close parentheses over denominator sin 140 to the power of o end fraction equals fraction numerator 4 over denominator square root of 3 end fraction cross times fraction numerator sin 140 to the power of o over denominator sin 140 to the power of o end fraction equals fraction numerator 4 over denominator square root of 3 end fraction

Answered by satyajit samal | 27th May, 2015, 09:44: AM

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