If 3pi/4 < theta < pi and (whole sqr root in L.H.S )  2 cot theta + 1/sin^2 theta = K - cot theta  Find K 

Asked by Deepak Singh | 22nd Jul, 2014, 06:49: PM

Expert Answer:

square root of open parentheses 2 co t space theta plus fraction numerator 1 over denominator sin squared space theta end fraction close parentheses end root equals square root of open parentheses fraction numerator 2 cos space theta over denominator sin space theta end fraction plus fraction numerator 1 over denominator sin squared space theta end fraction close parentheses end root equals square root of open parentheses fraction numerator 1 plus sin space 2 theta over denominator sin squared space theta end fraction close parentheses end root equals square root of open parentheses fraction numerator sin space theta space plus space cos theta over denominator sin space theta end fraction close parentheses squared end root equals plus-or-minus open parentheses fraction numerator sin space theta space plus space cos theta over denominator sin space theta end fraction close parentheses equals plus-or-minus open parentheses 1 plus c o t space theta close parentheses  g i v e n space theta element of open parentheses fraction numerator 3 straight pi over denominator 4 end fraction comma space straight pi close parentheses space s o space a n s w e r space i s space minus left parenthesis 1 plus space c o t space theta right parenthesis space equals space minus 1 minus c o t space theta space equals space k minus c o t space theta space rightwards double arrow k equals minus 1

Answered by Dharma Teja | 23rd Jul, 2014, 08:47: AM

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