Question

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Answer 1

answer in attachment.

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Answer 2

Answer:

cos²A + cos²B - cos²C

= (1/2)(1+cos2A) + (1/2)(1+cos2B) - cos²(A+B)

= 1 + (1/2)(cos2A + cos2B) - cos²(A+B)

= 1 + cos(A+B)cos(A-B) - cos²(A+B)

= 1 + cos(A+B)[cos(A-B) - cos(A+B)]

= 1 + cos(A+B) 2sinAsinB

= 1 - 2sinAsinBcosC

cos(A+B) = cos(180-C) = -cosC

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Attn: You need to change sinC to cosC. Otherwise, this is not an identity. Counter example, A = B = 45, and C = 90.

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