Cos (A + B)+ Sin (A - B) = 2 Sin(45 + A) Cos (45 + B )
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Step-by-step explanation:
taking L.H.S.
= cosAcosB - sinAsinB + sinAcosB - cosAsinB
taking R.H.S.
= 2(sin45°cosA + cos45°sinA)(cos45cosB - sin45sinB)
= 2(√2/2cosA + √2/2sinA)(√2/2cosB - √2/2sinB)
= 2( (1/2)cosAcosB - (1/2)cosAsinB + (1/2)sinAcosB - (1/2)sinAsinB)
= cosAcosB - cosAsinB + sinAcosB - sinAsinB
hence L.H.S. = R.H.S.
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