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CBSE Class 10 Answered

Q27. If sec ϴ + tan ϴ = x, show that sin ϴ =    I haven't understand the solution of this question.Will u please explain me
Asked by shivkant.928 | 21 Dec, 2018, 11:19: PM
answered-by-expert Expert Answer
we have, sec2θ - tan2θ = 1
 
begin mathsize 12px style s e c left parenthesis theta right parenthesis space minus space tan left parenthesis theta right parenthesis space equals space fraction numerator 1 over denominator s e c open parentheses theta close parentheses plus tan open parentheses theta close parentheses end fraction space space equals space 1 over x
s e c open parentheses theta close parentheses plus tan open parentheses theta close parentheses space equals space x space..................... left parenthesis 1 right parenthesis
s e c left parenthesis theta right parenthesis space minus space tan left parenthesis theta right parenthesis space equals space 1 over x space................... left parenthesis 2 right parenthesis
B y space a d d i n g space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space g e t space comma space space space 2 space s e c open parentheses theta close parentheses space equals space x space plus 1 over x space space o r space space space s e c open parentheses theta close parentheses space equals 1 half open parentheses x plus 1 over x close parentheses space............. left parenthesis 3 right parenthesis
B y space s u b t r a c t i n g space left parenthesis 2 right parenthesis space f r o m space left parenthesis 1 right parenthesis comma space w e space g e t comma space space space 2 space tan open parentheses theta close parentheses space equals space x space minus 1 over x space space o r space space tan open parentheses theta close parentheses space equals space 1 half open parentheses x space minus space 1 over x close parentheses space............ left parenthesis 4 right parenthesis space
B y space d i v i d i n g space e q n. left parenthesis 4 right parenthesis space b y space e q n. left parenthesis 3 right parenthesis comma space space w e space g e t comma space space fraction numerator tan open parentheses theta close parentheses over denominator s e c open parentheses theta close parentheses end fraction space equals space fraction numerator begin display style bevelled fraction numerator sin open parentheses theta close parentheses over denominator cos open parentheses theta close parentheses end fraction end style over denominator begin display style bevelled fraction numerator 1 over denominator cos open parentheses theta close parentheses end fraction end style end fraction space equals space sin open parentheses theta close parentheses space equals space fraction numerator 1 half open parentheses x space minus space 1 over x close parentheses over denominator 1 half open parentheses x plus 1 over x close parentheses end fraction space equals space fraction numerator x squared minus 1 over denominator x squared plus 1 end fraction end style
Answered by Thiyagarajan K | 22 Dec, 2018, 12:01: AM
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