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Home / Doubts and Solutions/JUNIOR/Class 6/Mathematics

if tan A = n tan B  and sin A = m sin B, PROVE THAT COS SQUARE A = m2 - 1 / n2 - 1

Asked by nisha_vini29 7th September 2015, 6:21 PM
Answered by Expert
Answer:

fraction numerator t a n A over denominator t a n B end fraction equals n fraction numerator s i n A c o s B over denominator c o s A s i n B end fraction equals n..... left parenthesis i right parenthesis fraction numerator s i n A over denominator s i n B end fraction equals m s i n A space equals space m space s i n B f r o m left parenthesis i right parenthesis therefore fraction numerator c o s B over denominator c o s A end fraction equals n over m m c o s B equals n c o s A n squared c o s squared A equals m squared c o s squared B space space space space space space space space space space space space space space equals m squared open parentheses 1 minus s i n squared B close parentheses space space space space space space space space space space space space space space space space equals m squared open parentheses 1 minus fraction numerator s i n squared A over denominator m squared end fraction close parentheses space space space space space space space space space space space space space space space space space equals m squared minus s i n squared A space space space space space space space space space space space space space space space space space equals m squared minus 1 plus c o s squared A therefore n squared c o s squared A minus c o s squared A equals m squared minus 1 therefore c o s squared A equals fraction numerator m squared minus 1 over denominator n squared minus 1 end fraction

Answered by Expert 7th September 2015, 6:34 PM
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