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ICSE Class 10 Answered

eliminate ß in the following epressions. tan ß + sin ß = p  and  tan ß - sin ß = q
Asked by nidhimehendre | 25 Dec, 2018, 10:02: PM
answered-by-expert Expert Answer
tan ß + sin ß = p  .....(i)
tan ß - sin ß = q ......(ii)
Solving (i) and (ii) we get
tan ß = (p + q)/2 and sin ß = (p - q)/2 ......(iii)
Multiplying (i) and (ii)
tan2 ß - sin2 ß = pq
 
 
begin mathsize 16px style fraction numerator sin squared straight beta over denominator cos squared straight beta end fraction minus sin squared straight beta equals pq
sin squared straight beta open parentheses fraction numerator 1 over denominator cos squared straight beta end fraction minus 1 close parentheses equals pq
fraction numerator begin display style sin squared straight beta end style over denominator begin display style cos squared straight beta end style end fraction open parentheses 1 minus cos squared straight beta close parentheses equals pq
tan squared βsin squared straight beta equals pq
open parentheses fraction numerator straight p plus straight q over denominator 2 end fraction close parentheses squared cross times open parentheses fraction numerator begin display style straight p minus straight q end style over denominator begin display style 2 end style end fraction close parentheses squared equals pq
open parentheses straight p plus straight q close parentheses squared open parentheses straight p minus straight q close parentheses squared equals 16 pq
open parentheses straight p squared minus straight q squared close parentheses squared equals 16 pq


end style
 
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