sin‌pxcosqx‌dx=0 ‌‌‌a=m+n+p,b=m+n+q From Eq. (i), we know that
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f(x)‌dx=4‌
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f(x) Iffis periodic withπand symmetric in all four quadrants ⇒‌‌mandnare even
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sin‌pxcosnx‌dx=0 ⇒Integrand is odd over symmetric interval[0,2π] Since, n is even so,pis odd also, ‌
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sin‌pxcosqx‌dx=0 ‌⇒‌‌sin‌pxcosqx‌ is odd about ‌x=‌
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‌⇒‌‌q‌ is odd ‌ ‌‌‌∴a=m+n+p ‌‌‌=‌ even ‌+‌ even ‌+‌ odd ‌=‌ odd ‌ ‌‌ And ‌b=m+n+p ‌‌‌=‌ even ‌+‌ even ‌+‌ odd ‌=‌ odd ‌