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CBSE Class 10 Answered

Prove that Sin theta(1+tan theta) +cos theta(1+cos theta)=sec theta + cosec yheta
Asked by Nimmi | 28 Feb, 2019, 01:05: AM
answered-by-expert Expert Answer
begin mathsize 12px style L H S space equals space sin theta left parenthesis 1 plus tan theta right parenthesis plus cos theta left parenthesis 1 plus c o t space theta right parenthesis space
L H S space equals space sin theta open parentheses 1 plus fraction numerator sin theta over denominator cos theta end fraction close parentheses plus space cos theta open parentheses 1 plus fraction numerator cos space theta over denominator sin space theta end fraction close parentheses space equals space fraction numerator sin space theta open parentheses cos space theta space plus sin space theta close parentheses over denominator cos theta end fraction space plus space fraction numerator cos space theta open parentheses sin space theta space plus space cos space theta close parentheses over denominator sin space theta end fraction
L H S space equals space fraction numerator sin squared theta space open parentheses cos space theta space plus sin space theta close parentheses space plus space cos squared theta open parentheses cos space theta space plus sin space theta close parentheses over denominator sin space theta space cos space theta end fraction space equals space fraction numerator sin cubed theta space plus cos cubed theta space plus sin theta space cos theta open parentheses sin theta plus cos theta close parentheses over denominator sin space theta space cos space theta end fraction
L H S space equals space fraction numerator open parentheses sin theta plus cos theta close parentheses open parentheses sin squared theta space minus space sin theta space cos theta space plus space cos squared theta close parentheses space plus space sin theta space cos space theta left parenthesis sin theta space plus space cos theta space right parenthesis over denominator sin space theta space cos space theta end fraction
L H S space equals space fraction numerator open parentheses sin theta plus cos theta close parentheses open parentheses 1 space minus space sin theta space cos theta space close parentheses space plus space sin theta space cos space theta left parenthesis sin theta space plus space cos theta space right parenthesis over denominator sin space theta space cos space theta end fraction space equals space fraction numerator open parentheses sin theta plus cos theta close parentheses over denominator sin space theta space cos space theta end fraction space equals space fraction numerator 1 over denominator cos space theta end fraction plus fraction numerator 1 over denominator sin space theta end fraction space equals space s e c space theta space plus space cos e c space theta
L H S space equals space R H S end style
Answered by Thiyagarajan K | 28 Feb, 2019, 11:00: AM
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