Q) Let y=f(x) , f colon R rightwards arrow R space b e space a n space o d d space d i f f e r e n t i a b l e space f u n c t i o n space s u c h space t h a t space f apostrophe apostrophe apostrophe left parenthesis x right parenthesis greater than 0 space & space g left parenthesis alpha comma beta right parenthesis equals sin to the power of 8 alpha plus cos to the power of 8 beta plus 2 minus 4 sin squared alpha cos squared beta. I f space f " left parenthesis g left parenthesis alpha comma beta right parenthesis right parenthesis equals 0 comma space t h e n space space p r o v e space t h a t space sin squared alpha plus sin squared beta space i s space e q u a l space t o space 1.

Asked by araima2001 | 2nd Jul, 2017, 02:38: AM

Expert Answer:

begin mathsize 16px style Odd space differential space function space means
function space is space odd
straight f apostrophe left parenthesis straight x right parenthesis equals fraction numerator df left parenthesis straight x right parenthesis over denominator dx end fraction
equals fraction numerator straight d open parentheses negative straight f left parenthesis negative straight x right parenthesis close parentheses over denominator dx end fraction
equals negative fraction numerator straight d open parentheses straight f left parenthesis negative straight x right parenthesis close parentheses over denominator dx end fraction
equals negative open parentheses negative straight f apostrophe open parentheses negative straight x close parentheses close parentheses
equals straight f apostrophe open parentheses negative straight x close parentheses
Use space this space and space second space derivative space test space to space prove space it end style

Answered by Sneha shidid | 4th Jul, 2017, 10:57: AM