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CBSE Class 12-science Answered

If (1-y2)1/2+(1-t2)1/2=a(y-t)  and  x=sin-1[t(1-t)1/2+(t1/2)((1-t2))1/2, ​ prove that dy/dx=[2(t)1/2(1-y2)1/2]/[2(t)1/2+(1+t)1/2]  
Asked by soumen_tiku | 30 Jun, 2018, 11:58: AM
answered-by-expert Expert Answer
begin mathsize 16px style square root of 1 minus straight y squared end root plus square root of 1 minus straight t squared end root equals straight a open parentheses straight y minus straight t close parentheses...... diff space wrt space to space left parenthesis straight t right parenthesis
1 half cross times fraction numerator 1 over denominator square root of 1 minus straight y squared end root end fraction cross times negative 2 straight y cross times dy over dt plus 1 half cross times fraction numerator 1 over denominator square root of 1 minus straight t squared end root end fraction cross times negative 2 straight t equals straight a dy over dt
dy over dt equals fraction numerator fraction numerator negative straight t over denominator square root of 1 minus straight t squared end root end fraction over denominator straight a plus fraction numerator straight y over denominator square root of 1 minus straight y squared end root end fraction end fraction

sinx space equals straight t cross times open parentheses square root of 1 minus straight t squared end root close parentheses plus open parentheses square root of straight t close parentheses open parentheses square root of 1 minus straight t squared end root close parentheses...... diff space wrt space to space left parenthesis straight t right parenthesis
dx over dt cross times cos space straight x space equals space open parentheses open parentheses square root of 1 minus straight t squared end root close parentheses plus 1 half cross times fraction numerator 1 over denominator square root of 1 minus straight t squared end root end fraction cross times negative 2 straight t cross times open parentheses square root of 1 minus straight t squared end root close parentheses close parentheses plus open parentheses fraction numerator 1 over denominator 2 square root of straight t end fraction open parentheses square root of 1 minus straight t squared end root close parentheses plus 1 half cross times fraction numerator 1 over denominator square root of 1 minus straight t squared end root end fraction cross times negative 2 straight t cross times open parentheses square root of straight t close parentheses close parentheses
dx over dt cross times cos space straight x space equals space open parentheses open parentheses square root of 1 minus straight t squared end root close parentheses minus straight t close parentheses plus open parentheses fraction numerator 1 over denominator 2 square root of straight t end fraction open parentheses square root of 1 minus straight t squared end root close parentheses minus fraction numerator 1 over denominator square root of 1 minus straight t squared end root end fraction cross times straight t cross times open parentheses square root of straight t close parentheses close parentheses
dy over dx equals fraction numerator dy over dt over denominator dy over dt end fraction end style
Answered by Arun | 06 Jul, 2018, 12:04: PM
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