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Mathematics
Pongo
23 May, 04:24
Prove
that
2 cos (A + 45°) cos (B-45°) = cos 2A
+2
Answers (
1
)
Calvin
23 May, 04:45
0
Step-by-step explanation:
2 cos (A+45) cos (B-45)
=2[cos A cos 45-sin A sin 45][cos B cos 45+sin B sin 45]
=2[cos A * 1/√2-sin A * 1/√2][cos B*1/√2+sin B*1/√2]
=2[1/√2 (cos A-sin A) ][1/√2 (cos B-sin B]
=2*1/√2*1/√2 (cos A-sin A) (cos B+sin B)
=cosA cos B+cos A sin B-sin A cos B-sin A sin B
=cos A cos B-sin A sin B - (sin A cos B-cos A sin B)
=cos (A+B) - sin (A-B)
i think there should be A in place of B.
then
=cos (A+A) - sin (A-A)
=cos 2A-sin 0
=cos 2A
as sin 0=0
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