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CBSE Class 10 Answered

xsin 3+ycos 3θ=sinθcosθ.   Xcosθ=ysinθ.  Show that x2 +y2=1  
Asked by drindhusrmc | 10 Feb, 2019, 08:18: AM
answered-by-expert Expert Answer
begin mathsize 12px style x space sin cubed theta space plus space y space cos cubed theta space equals space sin theta space cos theta space................. left parenthesis 1 right parenthesis
x space cos theta space equals space y space sin theta space.................. left parenthesis 2 right parenthesis
s u b s t i t u t i n g space f o r space cos theta space f r o m space e q n. left parenthesis 2 right parenthesis space i n space e q n. left parenthesis 1 right parenthesis comma space w e space g e t
x space sin cubed theta space plus space y open parentheses y cubed over x cubed close parentheses sin cubed theta space equals space y over x sin squared theta
x to the power of 4 sin theta space plus space y to the power of 4 sin theta space equals space x squared y space space space space space o r space space space sin theta space equals space fraction numerator x squared y over denominator open parentheses space x to the power of 4 plus y to the power of 4 space close parentheses end fraction............. left parenthesis 2 right parenthesis
S i m i l a r l y space b y space s u b s t i t u t i n g space f o r space sin theta space f r o m space e q n. left parenthesis 2 right parenthesis space i n space e q n. left parenthesis 1 right parenthesis comma space w e space g e t
cos theta space equals space fraction numerator x y squared over denominator open parentheses space x to the power of 4 plus y to the power of 4 space close parentheses end fraction space space.............. left parenthesis 3 right parenthesis
u sin g space t h e space i d e n t i t y space sin squared theta space plus space cos squared theta space equals space 1 space a n d space u sin g space e q n s. space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space g e t

fraction numerator x to the power of 4 y squared plus x squared y to the power of 4 over denominator open parentheses space x to the power of 4 plus y to the power of 4 space close parentheses squared end fraction space equals space 1 space space space space space space h e n c e space space w e space g e t comma space space space space space space space space space x squared plus y squared space equals space fraction numerator open parentheses space x to the power of 4 plus y to the power of 4 space close parentheses squared over denominator x squared y squared end fraction
end style
Answered by Thiyagarajan K | 12 Feb, 2019, 12:42: PM
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