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CBSE Class 12-science Answered

Find the sum of the max. and min values of 1/1+(2cosx-4sinx)^2 
Asked by puneetgarg2555 | 01 May, 2019, 10:32: AM
answered-by-expert Expert Answer
L e t space f left parenthesis x right parenthesis equals fraction numerator 1 over denominator 1 plus left parenthesis 2 cos x minus 4 sin x right parenthesis squared end fraction S i n c e comma space minus 1 less or equal than cos x less or equal than 1 space a n d space minus 1 less or equal than sin x less or equal than 1 rightwards double arrow negative 2 less or equal than 2 cos x less or equal than 2 space a n d space minus 4 less or equal than 4 sin x less or equal than 4 rightwards double arrow negative 2 less or equal than 2 cos x less or equal than 2 space a n d space minus 4 less or equal than negative 4 sin x less or equal than 4 rightwards double arrow negative 6 less or equal than 2 cos x minus 4 sin x less or equal than 6 rightwards double arrow left parenthesis 2 cos x minus 4 sin x right parenthesis squared less or equal than 36 A l s o comma space left parenthesis 2 cos x minus 4 sin x right parenthesis squared greater or equal than 0 rightwards double arrow 1 plus left parenthesis 2 cos x minus 4 sin x right parenthesis squared greater or equal than 1 rightwards double arrow fraction numerator 1 over denominator 1 plus left parenthesis 2 cos x minus 4 sin x right parenthesis squared end fraction less or equal than 1 space a n d space fraction numerator 1 over denominator 1 plus left parenthesis 2 cos x minus 4 sin x right parenthesis squared end fraction greater or equal than 1 over 37 T h e space m i n space v a l u e space i s space 1 over 37 space a n d space m a x i m u m space v a l u e space i s space 1 S u m space o f space m i n space a n d space m a x space v a l u e s space i s space 1 over 37 plus 1 equals 38 over 37
Answered by Renu Varma | 01 May, 2019, 04:10: PM

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CBSE 12-science - Maths
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