Asked by Om Kumar | 8th Jun, 2014, 10:18: AM

Expert Answer:

H e r e space i t space i s space g i v e n space t h a t space s e c theta space equals space 5 over 4

s e c theta equals 5 over 4 equals fraction numerator h y p over denominator a d j end fraction rightwards double arrow cos theta space equals 4 over 5 N o w comma space sin squared theta space plus space cos squared theta space equals space 1 rightwards double arrow space sin squared theta space plus space open parentheses 4 over 5 close parentheses squared equals 1 rightwards double arrow sin squared theta equals space 1 space minus space 16 over 25 rightwards double arrow sin squared theta equals space 9 over 25 rightwards double arrow sin theta equals space 3 over 5 N e x t comma space tan theta space equals space fraction numerator sin theta over denominator cos theta end fraction equals space fraction numerator begin display style 3 over 5 end style over denominator begin display style 4 over 5 end style end fraction equals space 3 over 4 c o t theta space equals space fraction numerator 1 over denominator tan theta end fraction space equals space 4 over 3  S u b s t i t u t i n g space t h e space v a l u e s space i n space L. H. S. comma L. H. S. space equals space fraction numerator sin theta space minus space 2 cos theta over denominator tan theta space minus space c o t theta end fraction equals space fraction numerator begin display style 3 over 5 end style space minus space 2 space x begin display style 4 over 5 end style over denominator begin display style 3 over 4 end style space minus space begin display style 4 over 3 end style end fraction space equals space fraction numerator begin display style 3 over 5 end style space minus space begin display style 8 over 5 end style over denominator begin display style fraction numerator 9 space minus space 16 over denominator 12 space end fraction end style end fraction space equals space fraction numerator begin display style fraction numerator minus 5 over denominator 5 end fraction end style over denominator begin display style fraction numerator minus 7 over denominator 12 end fraction end style end fraction space equals space fraction numerator 1 over denominator begin display style 7 over 12 end style end fraction space equals space 12 over 7 space equals space R. H. S. H e n c e space fraction numerator sin theta space minus space 2 cos theta over denominator tan theta space minus space c o t theta end fraction equals space 12 over 7

Answered by Mili Hariyani | 9th Jun, 2014, 11:06: AM

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