Question

cos²π/12+cos²π/4+cos²5π/12​
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Answer 1

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Answer 2

Solution :

⇒ cos²5π/12+cos²(π/12+5π/12)+cos5π/12×cosπ/12

⇒ cos²(3π/12+2π/12)+cos²π/2+cos(3π/12+2π/12)×cos(3π/12-2π/12)

⇒ cos²(π/4+π/6)+cos(π/4+π/6)×cos(π/4-π/6)

⇒ cos(π/4+π/6)[cos(π/4+π/6)+cos(π/4-π/6)]

⇒ (√6-√2)/4[(√6-√2)/4+(√6+√2)/4]

⇒ (√6-√2)/4x(√6/2)

⇒ (6-2√3)/8

⇒ (3-√3)/4