JEE Class main Answered
Let x, y, z be real numbers with ![x greater or equal than y greater or equal than z](https://www.topperlearning.com/public/wiris/ckeditor4/plugins/ckeditor_wiris/integration/showimage.php?formula=f758c3cd4116bc6e3fc8f18838ac6a58)
such that x+y+z=
and P = cosx.siny.cosz. then what are the minimum and maximum values of P? Also mention at what values of x,y,z they occur?
Asked by sarn1027 | 05 May, 2020, 14:44: PM
Given:
x+y+z=
... (ii)
P = cosx siny cosz
![rightwards double arrow P equals fraction numerator cos z over denominator 2 end fraction open parentheses 2 space cos x space sin y close parentheses
rightwards double arrow P equals fraction numerator cos z over denominator 2 end fraction open square brackets sin open parentheses x plus y close parentheses minus sin open parentheses x minus y close parentheses close square brackets less or equal than fraction numerator cos z over denominator 2 end fraction space sin open parentheses x plus y close parentheses
rightwards double arrow P less or equal than fraction numerator cos z over denominator 2 end fraction space sin open parentheses straight pi over 2 minus z close parentheses space space... space U sin g space left parenthesis i i right parenthesis
rightwards double arrow P less or equal than fraction numerator cos z over denominator 2 end fraction space cos z
rightwards double arrow P less or equal than fraction numerator cos squared z over denominator 2 end fraction equals 1 half cross times fraction numerator open parentheses 1 plus cos 2 z close parentheses over denominator 2 end fraction equals fraction numerator open parentheses 1 plus cos 2 z close parentheses over denominator 4 end fraction
rightwards double arrow P less or equal than 1 fourth open parentheses 1 plus cos straight pi over 6 close parentheses space space... space U sin g space left parenthesis i right parenthesis
rightwards double arrow P less or equal than 1 fourth open parentheses 1 plus fraction numerator square root of 3 over denominator 2 end fraction close parentheses
rightwards double arrow P less or equal than fraction numerator square root of 3 plus 2 over denominator 8 end fraction](https://images.topperlearning.com/topper/tinymce/cache/6fe349403b72dd5426054b82b08f1aad.png)
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