Evaluate fraction numerator left square bracket s e c theta c o s e c left parenthesis 90 minus theta right parenthesis minus t a n theta c o t left parenthesis 90 minus theta right parenthesis plus s i n squared 55 degree s i n squared 35 degree right square bracket over denominator left parenthesis tan 10 degree tan 20 degree tan 60 degree tan 70 degree tan 80 degree right parenthesis end fraction

Asked by pkirankumar4321 | 19th Sep, 2015, 08:51: PM

Expert Answer:

begin mathsize 14px style fraction numerator s e c theta cos e c left parenthesis 90 minus theta right parenthesis minus tan theta c o t left parenthesis 90 minus theta right parenthesis plus sin squared 55 plus sin squared 35 over denominator tan 10. tan 20. tan 60. tan 70. tan 80 end fraction equals fraction numerator s e c theta s e c theta minus t a n theta tan theta plus s i n squared 55 plus s i n squared left parenthesis 90 minus 55 right parenthesis over denominator t a n 10. t a n 20. t a n 60. t a n left parenthesis 90 minus 20 right parenthesis. t a n left parenthesis 90 minus 10 right parenthesis end fraction equals fraction numerator s e c squared theta minus t a n squared theta plus s i n squared 55 plus cos squared 55 over denominator t a n 10. t a n 20. square root of 3. c o t 20. c o t 10 end fraction equals fraction numerator 1 plus tan squared theta minus t a n squared theta plus 1 over denominator t a n 10. t a n 20. square root of 3. begin display style fraction numerator 1 over denominator tan 20 end fraction end style. begin display style fraction numerator 1 over denominator tan 10 end fraction end style end fraction equals fraction numerator 2 over denominator square root of 3 end fraction end style

Answered by Rashmi Khot | 20th Sep, 2015, 03:18: PM