Solve the differential equation $\dfrac{{dy}}{{dx}} + y\tan x = {\cos ^3}x$ If the HCF of \[408\] and $1032$ is expressible in the form $1032m - 408 \times 5$, find $m$
Answer
Verified
Hint: Here we find the HCF of given numbers by using Euclid’s division Algorithm . By using Euclid’s Division Algorithm lets us find the HCF of given numbers Euclid’s Division Algorithm: Dividend =divisor$ \times $quotient$ + $remainder Here larger number will be the dividend and smaller number will be the divisor $1032 = 408 \times 2 + 216$ $408 = 216 \times 1 + 192$ $216 = 192 \times 1 + 24$ $192 = 24 \times 8 + 0$ Since here the remainder is $0$ Therefore HCF of $1032$ and$408$ is $24$ Now let us equate the given form with HCF of given numbers $1032m - 408 \times 5$=$24$ $1032m = 2064$ $m = 2$ So here value of $m = 2$
NOTE: We can also find the HCF of two numbers by division method by dividing the larger number with the smaller number.
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