If SIN a =  21
                29
 
evaluate              SEC a           
                     TAN a - SIN a           
 
 
 

Asked by Shivam Mishra | 16th Sep, 2014, 03:23: PM

Expert Answer:

G i v e n space t h a t space sin a equals 21 over 29 W e space n e e d space t o space e v a l u a t e space fraction numerator s e c a over denominator tan a minus sin a end fraction W e space k n o w space t h a t space cos a equals square root of 1 minus sin squared a end root S i n c e space sin a equals 21 over 29 comma space w e space h a v e comma cos a equals square root of 1 minus open parentheses 21 over 29 close parentheses squared end root rightwards double arrow cos a equals square root of fraction numerator 29 squared minus 21 squared over denominator 29 squared end fraction end root rightwards double arrow cos a equals square root of fraction numerator 841 minus 441 over denominator 841 end fraction end root rightwards double arrow cos a equals square root of 400 over 841 end root rightwards double arrow cos a equals 20 over 29 T h u s comma space s e c a equals 29 over 20 space a n d space tan a equals fraction numerator sin a over denominator cos a end fraction equals fraction numerator 21 over 29 over denominator 20 over 29 end fraction equals 21 over 20 T h e r e f o r e comma space t h e space g i v e n space e x p r e s s i o n space i s comma fraction numerator s e c a over denominator tan a minus sin a end fraction equals fraction numerator begin display style 29 over 20 end style over denominator begin display style 21 over 20 end style minus begin display style 21 over 29 end style end fraction rightwards double arrow fraction numerator s e c a over denominator tan a minus sin a end fraction equals fraction numerator begin display style 29 over 20 end style over denominator begin display style fraction numerator 21 cross times 29 minus 21 cross times 20 over denominator 20 cross times 29 end fraction end style end fraction rightwards double arrow fraction numerator s e c a over denominator tan a minus sin a end fraction equals fraction numerator 29 cross times 29 over denominator 21 cross times 29 minus 21 cross times 20 end fraction rightwards double arrow fraction numerator s e c a over denominator tan a minus sin a end fraction equals fraction numerator 29 squared over denominator 21 cross times open parentheses 29 minus 20 close parentheses end fraction rightwards double arrow fraction numerator s e c a over denominator tan a minus sin a end fraction equals fraction numerator 841 over denominator 21 cross times 9 end fraction rightwards double arrow fraction numerator s e c a over denominator tan a minus sin a end fraction equals 841 over 189

Answered by Vimala Ramamurthy | 17th Sep, 2014, 08:58: AM