(Sin0+cos0)2+(cos0+cosec0)2=(1+sec0cosec0)2

Asked by Tejas Kulkarni | 13th Sep, 2014, 07:50: PM

Expert Answer:

Dear Student,
 
There is a minor correction in the question. The question should be as follows:
 
left parenthesis sin theta space plus space s e c theta right parenthesis squared space plus space left parenthesis cos theta space plus space cos e c theta right parenthesis squared space equals space left parenthesis 1 space plus space s e c theta cos e c theta right parenthesis squared
L. H. S. space equals space left parenthesis sin theta space plus space s e c theta right parenthesis squared space plus space left parenthesis cos theta space plus space cos e c theta right parenthesis squared equals space bottom enclose sin squared theta end enclose space plus space 2 sin theta s e c theta space plus space s e c squared theta space plus space bottom enclose cos squared straight theta end enclose space plus space 2 cos theta cos e c theta space plus space cos e c squared theta equals space 1 space plus space 2 sin theta s e c theta space plus space s e c squared theta space plus space 2 cos theta cos e c theta space plus cos e c squared theta equals space 1 space plus space 2 fraction numerator sin theta over denominator cos theta end fraction plus open parentheses fraction numerator 1 over denominator cos squared theta end fraction close parentheses space plus space 2 fraction numerator cos theta over denominator sin theta end fraction plus open parentheses fraction numerator 1 over denominator sin squared theta end fraction close parentheses equals space 1 space plus space 2 open square brackets fraction numerator sin theta over denominator cos theta end fraction plus fraction numerator cos theta over denominator sin theta end fraction close square brackets space plus space open square brackets fraction numerator 1 over denominator cos squared theta end fraction plus fraction numerator 1 over denominator sin squared theta end fraction close square brackets equals space 1 space plus space 2 open square brackets fraction numerator sin squared theta plus cos squared theta over denominator cos theta sin theta end fraction close square brackets space plus space space open square brackets fraction numerator sin squared theta space plus cos squared theta space over denominator cos squared theta sin squared theta end fraction close square brackets equals space 1 space plus space 2 open square brackets fraction numerator 1 over denominator cos theta sin theta end fraction close square brackets plus space open square brackets fraction numerator 1 over denominator cos squared theta sin squared theta end fraction close square brackets equals space 1 space plus space 2 s e c theta cos e c theta space plus space s e c squared theta cos e c squared theta equals space left parenthesis 1 space plus space s e c theta cos e c theta right parenthesis squared equals space R. H. S.

Answered by Mili Hariyani | 14th Sep, 2014, 12:46: AM

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