Question

Show that (sin C + cos C)2+(sin C-cos C)2 = 2
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Answer 1

Step-by-step explanation:

A, B formulae

2 sin A cos B = sin (A +B) +sin (A -B)

2 cos A sin B = sin (A +B) -sin (A -B)

2 cos A cos B = cos (A +B) +cos (A -B)

2 sin A sin B = cos (A -B) -cos (A +B)

C, D formulae

sin C +sin D = 2 sin (C +D)/2 cos (C -D)/2

sin C -sin D = 2 cos (C +D)/2 cos (C -D)/2

cos C +cos D = 2 cos (C +D)/2 cos (C -D)/2

cos C -cos D = - 2 sin (C +D)/2 sin (C -D)/2 = 2 sin (C+D)/2 sin (D - C)/2