tan theta/tan theta - tan 3 theta + cot theta/cot theta-cot 3 theta =

Asked by GURSHARNSUITS | 16th Jul, 2015, 02:16: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n colon fraction numerator tan theta over denominator tan theta minus tan 3 theta end fraction plus fraction numerator c o t theta over denominator c o t theta minus c o t 3 theta end fraction equals fraction numerator begin display style fraction numerator sin theta over denominator cos theta end fraction end style over denominator fraction numerator s i n theta over denominator c o s theta end fraction minus fraction numerator s i n 3 theta over denominator c o s 3 theta end fraction end fraction plus fraction numerator begin display style fraction numerator c o s theta over denominator sin theta end fraction end style over denominator fraction numerator c o s theta over denominator s i n theta end fraction minus fraction numerator c o s 3 theta over denominator s i n 3 theta end fraction end fraction equals fraction numerator begin display style fraction numerator s i n theta over denominator c o s theta end fraction end style over denominator fraction numerator s i n theta cross times c o s 3 theta minus sin 3 theta cross times c o s theta over denominator c o s theta cross times c o s 3 theta end fraction end fraction plus fraction numerator begin display style fraction numerator c o s theta over denominator s i n theta end fraction end style over denominator fraction numerator s i n 3 theta cross times c o s theta minus s i n theta cross times c o s 3 theta over denominator sin theta cross times sin 3 theta end fraction end fraction equals fraction numerator begin display style fraction numerator s i n theta over denominator c o s theta end fraction end style over denominator fraction numerator s i n open parentheses theta minus 3 theta close parentheses over denominator c o s theta cross times c o s 3 theta end fraction end fraction plus fraction numerator begin display style fraction numerator c o s theta over denominator s i n theta end fraction end style over denominator fraction numerator s i n open parentheses 3 theta minus theta close parentheses over denominator s i n theta cross times s i n 3 theta end fraction end fraction equals fraction numerator begin display style s i n theta cross times c o s 3 theta end style over denominator s i n open parentheses negative 2 theta close parentheses end fraction plus fraction numerator begin display style c o s theta cross times s i n 3 theta end style over denominator s i n open parentheses 2 theta close parentheses end fraction equals fraction numerator begin display style c o s theta cross times s i n 3 theta minus s i n theta cross times c o s 3 theta end style over denominator s i n open parentheses 2 theta close parentheses end fraction equals fraction numerator begin display style s i n open parentheses 3 theta minus theta close parentheses end style over denominator s i n open parentheses 2 theta close parentheses end fraction equals fraction numerator begin display style s i n open parentheses 2 theta close parentheses end style over denominator s i n open parentheses 2 theta close parentheses end fraction equals 1

Answered by Vimala Ramamurthy | 17th Jul, 2015, 09:20: AM