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begin mathsize 16px style g i v e n colon space left parenthesis a x divided by cos empty set right parenthesis plus left parenthesis b y divided by sin empty set right parenthesis space equals a 2 plus b 2
space space space space space space space space space space space space colon left parenthesis a x sin empty set divided by cos 2 empty set right parenthesis minus left parenthesis b y cos empty set divided by sin 2 empty set right parenthesis equals 0
t o space p r o o v e colon space left parenthesis a x right parenthesis 2 divided by 3 space plus space left parenthesis b y right parenthesis 2 divided by 3 space equals left parenthesis a 2 minus b 2 right parenthesis 2 divided by 3 end style
 
 
 

Asked by nk.pandit02 31st May 2016, 12:27 PM
Answered by Expert
Answer:
begin mathsize 12px style fraction numerator a x over denominator cos ϕ end fraction plus fraction numerator b y over denominator sin ϕ end fraction equals a squared plus b squared.... left parenthesis i right parenthesis

fraction numerator a x sin ϕ over denominator cos squared ϕ end fraction minus fraction numerator b y cos ϕ over denominator sin squared ϕ end fraction equals 0
rightwards double arrow fraction numerator a x s i n ϕ over denominator c o s squared ϕ end fraction equals fraction numerator b y c o s ϕ over denominator s i n squared ϕ end fraction
rightwards double arrow a x sin cubed ϕ equals b y cos cubed ϕ... left parenthesis i i right parenthesis

M u l t i p l y i n g space sin cubed ϕ space i n space t h e space f i r s t space e q u a t i o n comma space w e space g e t
fraction numerator a x sin cubed ϕ over denominator c o s ϕ end fraction plus fraction numerator b y sin cubed ϕ over denominator s i n ϕ end fraction equals open parentheses a squared plus b squared close parentheses sin cubed ϕ

U sin g space left parenthesis i i right parenthesis space i n space t h e space a b o v e space e q u a t i o n comma space w e space g e t
fraction numerator b y c o s cubed ϕ over denominator c o s ϕ end fraction plus b y sin squared ϕ equals open parentheses a squared plus b squared close parentheses s i n cubed ϕ
rightwards double arrow b y cos squared ϕ plus b y sin squared ϕ equals open parentheses a squared plus b squared close parentheses s i n cubed ϕ
rightwards double arrow b y open parentheses cos squared ϕ plus sin squared ϕ close parentheses equals open parentheses a squared plus b squared close parentheses s i n cubed ϕ
rightwards double arrow b y equals open parentheses a squared plus b squared close parentheses s i n cubed ϕ.... left parenthesis i i i right parenthesis
rightwards double arrow sin ϕ equals open parentheses fraction numerator b y over denominator a squared plus b squared end fraction close parentheses to the power of 1 divided by 3 end exponent
rightwards double arrow sin squared ϕ equals open parentheses fraction numerator b y over denominator a squared plus b squared end fraction close parentheses to the power of 2 divided by 3 end exponent.... left parenthesis i v right parenthesis
U sin g space left parenthesis i i i right parenthesis space i n space left parenthesis i i right parenthesis comma space w e space g e t
a x s i n cubed ϕ equals open parentheses a squared plus b squared close parentheses s i n cubed ϕ c o s cubed ϕ
rightwards double arrow c o s cubed ϕ equals fraction numerator a x over denominator a squared plus b squared end fraction
rightwards double arrow cos squared ϕ equals open parentheses fraction numerator a x over denominator a squared plus b squared end fraction close parentheses to the power of 2 divided by 3 end exponent... left parenthesis v right parenthesis

A d d i n g space left parenthesis i v right parenthesis space a n d space left parenthesis v right parenthesis comma space w e space g e t
s i n squared ϕ plus c o s squared ϕ equals open parentheses fraction numerator b y over denominator a squared plus b squared end fraction close parentheses to the power of 2 divided by 3 end exponent plus open parentheses fraction numerator a x over denominator a squared plus b squared end fraction close parentheses to the power of 2 divided by 3 end exponent
rightwards double arrow 1 equals open parentheses fraction numerator b y over denominator a squared plus b squared end fraction close parentheses to the power of 2 divided by 3 end exponent plus open parentheses fraction numerator a x over denominator a squared plus b squared end fraction close parentheses to the power of 2 divided by 3 end exponent
rightwards double arrow open parentheses a x close parentheses to the power of 2 divided by 3 end exponent plus open parentheses b y close parentheses to the power of 2 divided by 3 end exponent equals open parentheses a squared plus b squared close parentheses to the power of 2 divided by 3 end exponent



end style
Answered by Expert 1st June 2016, 11:59 AM
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