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CBSE Class 10 Answered

If l sin ϴ + m cos ϴ + n = 0 and l’ sin ϴ + m’ cos ϴ + n’ = 0 Then prove that (mn’-m’n)² + (nl’ – ln’)² = (lm’-l’m)²
Asked by CHIDAMBAR | 23 May, 2018, 07:00: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight l space sinθ space plus straight m space cosθ plus straight n equals 0...... left parenthesis 1 right parenthesis
straight l apostrophe space sinθ space plus straight m apostrophe space cosθ plus straight n apostrophe equals 0...... left parenthesis 2 right parenthesis
From space left parenthesis 1 right parenthesis
sinθ equals fraction numerator negative straight n minus straight m space cosθ over denominator straight l end fraction...... sub space in space left parenthesis 2 right parenthesis
straight l apostrophe space open parentheses fraction numerator negative straight n minus straight m space cosθ over denominator straight l end fraction close parentheses space plus straight m apostrophe space cosθ plus straight n apostrophe equals 0
cos space straight theta space equals space fraction numerator straight l apostrophe straight n minus ln apostrophe over denominator straight m apostrophe straight l minus ml apostrophe end fraction
sinθ equals open parentheses fraction numerator mn apostrophe minus straight m apostrophe straight n over denominator lm apostrophe minus straight l apostrophe straight m end fraction close parentheses
sin squared straight theta plus cos squared straight theta equals 1
open parentheses fraction numerator mn apostrophe minus straight m apostrophe straight n over denominator lm apostrophe minus straight l apostrophe straight m end fraction close parentheses squared plus open parentheses fraction numerator straight l apostrophe straight n minus ln apostrophe over denominator straight m apostrophe straight l minus ml apostrophe end fraction close parentheses squared equals 1
open parentheses mn apostrophe minus straight m apostrophe straight n close parentheses squared plus open parentheses straight l apostrophe straight n minus ln apostrophe close parentheses squared equals open parentheses lm apostrophe minus straight l apostrophe straight m close parentheses squared
end style
Answered by Arun | 24 May, 2018, 10:38: AM
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