if Xcos cubed + Ysin cubed = SIN A COS A AND XCOS A = YSIN A THEN X to the power of 2 space end exponent space plus space Y to the power of 2 space end exponent = 

Asked by aa610030 | 24th Nov, 2015, 07:18: PM

Expert Answer:

begin mathsize 11px style bold Xcos to the power of bold 3 bold A bold plus bold Ysin to the power of bold 3 bold A bold equals bold sinAcosA bold rightwards double arrow bold XcosA open parentheses bold cos to the power of bold 2 bold A close parentheses bold plus bold YsinA open parentheses bold sin to the power of bold 2 bold A close parentheses bold equals bold sinAcosA bold Using bold space bold XcosA bold space bold equals bold space bold Y bold space bold sinA bold space bold in bold space bold the bold space bold above bold space bold equation bold comma bold space bold we bold space bold get bold XcosA open parentheses bold cos to the power of bold 2 bold A close parentheses bold plus bold XcosA open parentheses bold sin to the power of bold 2 bold A close parentheses bold equals bold sinAcosA bold rightwards double arrow bold XcosA open parentheses bold cos to the power of bold 2 bold A bold plus bold sin to the power of bold 2 bold A close parentheses bold equals bold sinAcosA bold rightwards double arrow bold XcosA bold equals bold sinAcosA bold rightwards double arrow bold X bold equals bold sinA bold. bold. bold. bold. bold. bold left parenthesis bold 1 bold right parenthesis  bold Substituting bold space bold the bold space bold above bold space bold in bold space bold XcosA bold equals bold YsinA bold comma bold space bold we bold space bold get bold sinAcosA bold equals bold YsinA bold rightwards double arrow bold Y bold equals bold cosA bold. bold. bold. bold. bold left parenthesis bold 2 bold right parenthesis bold Using bold space bold left parenthesis bold 1 bold right parenthesis bold space bold and bold space bold left parenthesis bold 2 bold right parenthesis bold X to the power of bold 2 bold plus bold Y to the power of bold 2 bold equals bold sin to the power of bold 2 bold A bold plus bold cos to the power of bold 2 bold A bold equals bold 1 end style

Answered by satyajit samal | 25th Nov, 2015, 11:35: AM