Answer to Question #286290 in Trigonometry for EMILY

Question #286290

If cos(A-B) = cos 15° and cos(A+B)= cos 75° , the values of A and B. Hence without using a calculator and by using the sum and difference formula, show that cos 15° - cos 75° = 2 sin 45° sin 30°


1
Expert's answer
2022-01-11T00:21:25-0500

"A = 45^o \\space \\space B=30^o"

"-\\begin{cases}\n cos(A-B) = cosAcosB+sinAsinB=cos15^o \\\\\n cos(A+B) = cosAcosB-sinAsinB=cos75^o\n\\end{cases}"

"cos15^o-cos75^o=2sinAsinB=2sin45^osin30^o"


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