since m and l are real .it means that l<1 and m<1.(as if they were greater than 1 the square of the other would be complex)

hence write l = cosx (for some x)

and m is the sin x

then divide al+bm=c by sqrta^2+b^2 (As a^2 + b^2 is not 0)

write the lhs as sin(j+x) (for some j)

hence as the sin function oscillates between -1 and 1

c oscillates between -sqrt a^2 + b^2 to sqrt a^2+b^2

i know i didnt write clearly but hope u get what im saying
–
Pranav Chakravarthy
·
3 years, 11 months ago

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@Pranav Chakravarthy
–
yea, i got to what you are trying to say......it's great and right.....a good job...then wait for tomorrow for an another great problem......keep in touch....:--]
–
Raja Metronetizen
·
3 years, 11 months ago

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using cauchy-schwarz inequality,we have (a^2+b^2)(l^2+m^2)>=(al+bm)^2=c^2,which implies A
–
Sauvik Mondal
·
3 years, 11 months ago

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@Sauvik Mondal
–
good idea......you are then showing acumen over problem solving....great application...thanx.....
–
Raja Metronetizen
·
3 years, 11 months ago

@Raja Metronetizen
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It can be seen through this... most of the above portion ...
an expression of the form {Asinx +(or -) Bcosx} oscillates between +(-) sqrt(a^2 + b^2) ...
–
Saloni Gupta
·
3 years, 11 months ago

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TopNewestsince m and l are real .it means that l<1 and m<1.(as if they were greater than 1 the square of the other would be complex)

hence write l = cosx (for some x)

and m is the sin x

then divide al+bm=c by sqrta^2+b^2 (As a^2 + b^2 is not 0)

write the lhs as sin(j+x) (for some j)

hence as the sin function oscillates between -1 and 1

c oscillates between -sqrt a^2 + b^2 to sqrt a^2+b^2

i know i didnt write clearly but hope u get what im saying – Pranav Chakravarthy · 3 years, 11 months ago

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– Raja Metronetizen · 3 years, 11 months ago

yea, i got to what you are trying to say......it's great and right.....a good job...then wait for tomorrow for an another great problem......keep in touch....:--]Log in to reply

using cauchy-schwarz inequality,we have (a^2+b^2)(l^2+m^2)>=(al+bm)^2=c^2,which implies A – Sauvik Mondal · 3 years, 11 months ago

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– Raja Metronetizen · 3 years, 11 months ago

good idea......you are then showing acumen over problem solving....great application...thanx.....Log in to reply

The answer is a – Pranav Chakravarthy · 3 years, 11 months ago

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– Raja Metronetizen · 3 years, 11 months ago

how got to answer.....?..... :-oLog in to reply

– Saloni Gupta · 3 years, 11 months ago

It can be seen through this... most of the above portion ... an expression of the form {Asinx +(or -) Bcosx} oscillates between +(-) sqrt(a^2 + b^2) ...Log in to reply

– Raja Metronetizen · 3 years, 11 months ago

yes u r right.....Pranav c. himself described it rightly.......:)Log in to reply