prove that cos theta by 1-tan theta+sin theta by 1- cot theta equals to sin theta+ cos theta

Asked by gurunath196107 | 7th Apr, 2020, 04:21: PM

Expert Answer:

To prove: cos theta/ 1-tan theta + sin theta/ 1- cot theta = sin theta + cos theta
fraction numerator cos space straight theta over denominator 1 minus tan space straight theta end fraction plus fraction numerator sin space straight theta over denominator 1 minus cot space straight theta end fraction
equals fraction numerator cos space straight theta over denominator begin display style fraction numerator cos space straight theta minus sin space straight theta over denominator cos space straight theta end fraction end style end fraction plus fraction numerator sin space straight theta over denominator begin display style fraction numerator sin space straight theta minus cos space straight theta over denominator sin space straight theta end fraction end style end fraction
equals fraction numerator cos squared straight theta over denominator begin display style cos space straight theta minus sin space straight theta end style end fraction plus fraction numerator sin squared straight theta over denominator begin display style sin space straight theta minus cos space straight theta end style end fraction
equals fraction numerator cos squared straight theta minus sin squared straight theta over denominator begin display style cos space straight theta minus sin space straight theta end style end fraction
equals fraction numerator open parentheses cos space straight theta minus sin space straight theta close parentheses open parentheses cos space straight theta plus sin space straight theta close parentheses over denominator begin display style cos space straight theta minus sin space straight theta end style end fraction
equals sin space straight theta plus space cos space straight theta

Answered by Renu Varma | 7th Apr, 2020, 05:57: PM