Cos-1{sin /10 + sin 13/10} =?

Asked by Malavika Umesh | 3rd May, 2015, 07:28: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n colon cos to the power of negative 1 end exponent open curly brackets sin straight pi over 10 plus sin fraction numerator 13 straight pi over denominator 10 end fraction close curly brackets L e t space cos to the power of negative 1 end exponent open curly brackets sin straight pi over 10 plus sin fraction numerator 13 straight pi over denominator 10 end fraction close curly brackets equals x rightwards double arrow sin straight pi over 10 plus sin fraction numerator 13 straight pi over denominator 10 end fraction equals cos x rightwards double arrow 2 sin open parentheses fraction numerator fraction numerator 13 straight pi over denominator 10 end fraction plus straight pi over 10 over denominator 2 end fraction close parentheses cos open parentheses fraction numerator fraction numerator 13 straight pi over denominator 10 end fraction minus straight pi over 10 over denominator 2 end fraction close parentheses equals cos x rightwards double arrow 2 sin open parentheses fraction numerator 14 straight pi over denominator 20 end fraction close parentheses cos open parentheses fraction numerator 12 straight pi over denominator 20 end fraction close parentheses equals cos x rightwards double arrow 2 sin open parentheses fraction numerator 7 straight pi over denominator 10 end fraction close parentheses cos open parentheses fraction numerator 6 straight pi over denominator 10 end fraction close parentheses equals cos x rightwards double arrow 2 sin open parentheses 126 degree close parentheses cos open parentheses 108 degree close parentheses equals cos x rightwards double arrow 2 sin open parentheses straight pi over 2 plus 36 degree close parentheses cos open parentheses straight pi over 2 plus 18 degree close parentheses equals cos x rightwards double arrow negative 2 cos open parentheses 36 degree close parentheses sin open parentheses 18 degree close parentheses equals cos x rightwards double arrow negative 2 cross times fraction numerator square root of 5 plus 1 over denominator 4 end fraction cross times fraction numerator square root of 5 minus 1 over denominator 4 end fraction equals cos x rightwards double arrow negative 2 cross times 4 over 16 equals cos x rightwards double arrow negative 1 half equals cos x x equals cos to the power of negative 1 end exponent open parentheses negative 1 half close parentheses rightwards double arrow x equals fraction numerator 2 straight pi over denominator 3 end fraction

Answered by Vimala Ramamurthy | 5th May, 2015, 11:48: AM