if an angle  theta is divided int two parts such that the tangent of one part is k times the tangent of the other and x is their difference then find sin theta?

Asked by apurva151 | 21st Jun, 2015, 08:33: PM

Expert Answer:

L e t space theta space b e space d i v i d e d space i n t o space t w o space p a r t s space alpha space a n d space beta alpha plus beta equals theta open vertical bar alpha minus beta close vertical bar equals x tan alpha equals k tan beta fraction numerator tan alpha over denominator tan beta end fraction equals k over 1 rightwards double arrow fraction numerator tan alpha plus tan beta over denominator tan alpha minus tan beta end fraction equals fraction numerator k plus 1 over denominator k minus 1 end fraction rightwards double arrow fraction numerator begin display style fraction numerator sin alpha over denominator cos alpha end fraction end style plus begin display style fraction numerator sin beta over denominator cos beta end fraction end style over denominator fraction numerator sin alpha over denominator cos alpha end fraction minus fraction numerator sin beta over denominator cos beta end fraction end fraction equals fraction numerator k plus 1 over denominator k minus 1 end fraction rightwards double arrow fraction numerator sin alpha cos beta plus cos alpha sin beta over denominator sin alpha cos beta minus cos alpha sin beta end fraction equals fraction numerator k plus 1 over denominator k minus 1 end fraction rightwards double arrow fraction numerator sin open parentheses alpha plus beta close parentheses over denominator sin open parentheses alpha minus beta close parentheses end fraction equals fraction numerator k plus 1 over denominator k minus 1 end fraction rightwards double arrow sin theta equals sin open parentheses alpha minus beta close parentheses fraction numerator k plus 1 over denominator k minus 1 end fraction rightwards double arrow sin theta equals sin open parentheses plus-or-minus x close parentheses fraction numerator k plus 1 over denominator k minus 1 end fraction rightwards double arrow sin theta equals plus-or-minus sin x fraction numerator k plus 1 over denominator k minus 1 end fraction

Answered by satyajit samal | 22nd Jun, 2015, 02:37: AM

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