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Sir pls solve this question.

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Asked by rsudipto 15th December 2018, 6:13 PM
Answered by Expert
Answer:
begin mathsize 12px style A space equals space integral subscript 1 superscript sin theta end superscript fraction numerator t space d t over denominator 1 plus t squared end fraction space equals space 1 half integral subscript 1 superscript sin theta end superscript fraction numerator 2 t space d t over denominator 1 plus t squared end fraction space equals space open vertical bar ln square root of 1 plus t squared end root close vertical bar subscript 1 superscript sin theta end superscript space equals space ln open parentheses square root of fraction numerator 1 plus sin squared theta over denominator 2 end fraction end root space close parentheses
B space equals space integral subscript 1 superscript cos e c theta end superscript fraction numerator d t over denominator t open parentheses 1 plus t squared close parentheses end fraction space equals space integral subscript 1 superscript cos e c theta end superscript open parentheses 1 over t space minus space fraction numerator t over denominator 1 plus t squared end fraction close parentheses d t space equals space open square brackets ln space t space minus space ln space square root of 1 plus t squared end root close square brackets subscript 1 superscript cos e c theta end superscript
equals space ln space open square brackets fraction numerator t over denominator square root of 1 plus t squared end root end fraction close square brackets subscript 1 superscript cos e c theta end superscript space equals space ln open square brackets square root of fraction numerator 2 over denominator 1 plus sin squared theta end fraction end root space close square brackets

D space equals space open vertical bar table row A cell A squared end cell B row cell e to the power of A e to the power of B end cell cell B squared end cell cell negative 1 end cell row 1 cell open parentheses A squared plus B squared close parentheses end cell cell negative 1 end cell end table close vertical bar space equals space A open parentheses negative B squared plus A squared plus B squared close parentheses space minus A squared open parentheses negative e to the power of A e to the power of B space plus space 1 close parentheses space plus B open parentheses e to the power of A e to the power of B open parentheses A squared plus B squared close parentheses minus B squared close parentheses space.......... left parenthesis 1 right parenthesis
W e space h a v e comma space e to the power of A e to the power of B space end exponent space equals space square root of fraction numerator 1 plus sin squared theta over denominator 2 end fraction end root cross times square root of fraction numerator 2 over denominator 1 plus sin squared theta end fraction end root space equals 1........... left parenthesis 2 right parenthesis
u sin g space e q n. left parenthesis 2 right parenthesis space i n space e q n. left parenthesis 1 right parenthesis comma space space D space equals space A cubed space plus space A squared B space equals space A squared left parenthesis A plus B right parenthesis.......... left parenthesis 3 right parenthesis

w e space h a v e space comma space A plus B space equals space ln open parentheses square root of fraction numerator 1 plus sin squared theta over denominator 2 end fraction end root space close parentheses space plus space space ln open square brackets square root of fraction numerator 2 over denominator 1 plus sin squared theta end fraction end root space close square brackets space equals space 0
h e n c e space D space space equals space 0
space end style
Answered by Expert 16th December 2018, 11:49 AM
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