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cos²15 + cos²35 + cos²55 + cos²75
= cos²15 + cos²35 + sin²(90 - 55) + sin²(90 - 75)
= cos²15 + cos²35 + sin²35 + sin²15
= cos²15 + sin²15 + cos²35 + sin²35
cos²x + sin²x = 1
(cos²15 + sin²15) + (cos²35 + sin²35)
= 1 + 1
= 2