prove that :sin-3x/5+sin-4x/5=sin-x    

Asked by poojaparmar065 | 15th Sep, 2014, 11:04: AM

Expert Answer:

sin space to the power of minus 1 end exponent space open parentheses fraction numerator 3 x over denominator 5 end fraction close parentheses space plus space sin space to the power of minus 1 end exponent space open parentheses fraction numerator 4 x over denominator 5 end fraction close parentheses L e t space A space equals space sin space to the power of minus 1 end exponent space open parentheses fraction numerator 3 x over denominator 5 end fraction close parentheses comma space B space equals space sin space to the power of minus 1 end exponent space open parentheses fraction numerator 4 x over denominator 5 end fraction close parentheses s o comma space s i n space A space equals space fraction numerator 3 x over denominator 5 end fraction comma space sin space B equals fraction numerator 4 x over denominator 5 end fraction S i n space left parenthesis A plus B right parenthesis equals S i n space A space C o s space B space plus thin space C o s space A space S I n space B S I n space left parenthesis A plus B right parenthesis space equals space fraction numerator 3 x over denominator 5 end fraction cross times fraction numerator 3 x over denominator 5 end fraction plus fraction numerator 4 x over denominator 5 end fraction cross times fraction numerator 4 x over denominator 5 end fraction equals fraction numerator 25 x over denominator 25 end fraction equals x  S i n space left parenthesis A plus B right parenthesis equals x A plus B space equals space S i n space to the power of minus 1 end exponent space x  S u b s t i t u t e space t h e space v a l u e s space o f space A space a n d space B comma space w e space g e t  sin space to the power of minus 1 end exponent space open parentheses fraction numerator 3 x over denominator 5 end fraction close parentheses space plus space sin space to the power of minus 1 end exponent space open parentheses fraction numerator 4 x over denominator 5 end fraction close parentheses equals sin space to the power of minus 1 end exponent space x  H e n c e space P r o v e d

Answered by Dharma Teja | 16th Sep, 2014, 10:17: AM