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Asked by sweety | 12th Dec, 2015, 11:58: AM

Expert Answer:

C o n s i d e r space t h e space g i v e n space f u n c t i o n comma y equals cos to the power of negative 1 end exponent open parentheses fraction numerator 3 sin x plus 4 cos x over denominator 5 end fraction close parentheses... left parenthesis 1 right parenthesis W e space n e e d space t o space f i n d space fraction numerator d y over denominator d x end fraction F r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma cos y equals fraction numerator 3 s i n x plus 4 c o s x over denominator 5 end fraction... left parenthesis 2 right parenthesis D i f f e r e n t i a t i n g space t h e space a b o v e space f u n c t i o n space w i t h space r e s p e c t space t o space x comma space w e space h a v e comma minus sin y cross times fraction numerator d y over denominator d x end fraction equals fraction numerator 3 c o s x minus 4 sin x over denominator 5 end fraction rightwards double arrow s i n y cross times fraction numerator d y over denominator d x end fraction equals fraction numerator 4 s i n x minus 3 c o s x over denominator 5 end fraction... left parenthesis 3 right parenthesis C o n s i d e r space e q u a t i o n space left parenthesis 2 right parenthesis S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a c o s squared y equals open parentheses 3 sin x plus 4 cos x close parentheses squared over 25 rightwards double arrow 1 minus c o s squared y equals 1 minus open parentheses 3 s i n x plus 4 c o s x close parentheses squared over 25 rightwards double arrow 1 minus c o s squared y equals fraction numerator 25 minus open parentheses 3 s i n x plus 4 c o s x close parentheses squared over denominator 25 end fraction rightwards double arrow sin squared y equals fraction numerator 25 minus open parentheses 3 s i n x plus 4 c o s x close parentheses squared over denominator 25 end fraction rightwards double arrow s i n y equals fraction numerator square root of 25 minus open parentheses 3 sin x plus 4 cos x close parentheses squared end root over denominator 5 end fraction... left parenthesis 4 right parenthesis S u b s t i t u t i n g space t h e space v a l u e space o f space sin y space f r o m space e q u a t i o n space left parenthesis 4 right parenthesis space i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma fraction numerator square root of 25 minus open parentheses 3 s i n x plus 4 c o s x close parentheses squared end root over denominator 5 end fraction cross times fraction numerator d y over denominator d x end fraction equals fraction numerator 4 s i n x minus 3 c o s x over denominator 5 end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator 4 s i n x minus 3 c o s x over denominator square root of 25 minus open parentheses 3 s i n x plus 4 c o s x close parentheses squared end root end fraction

Answered by Vimala Ramamurthy | 12th Dec, 2015, 03:03: PM