Question

Find the greatest value of cos²(π/8+x/2)+cos²(π/8-x/2) .

Please answer.

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Answer 1

Let us consider the LHS

sin2(π/8 + x/2) – sin2(π/8 – x/2)

sin2(π/8 + x/2) – sin2(π/8 – x/2) = sin (π/8 + x/2 + π/8 – x/2) sin (π/8 + x/2 – (π/8 – x/2)

= sin (π/8 + π/8) sin (π/8 + x/2 – π/8 + x/2)

= sin π/4 sin x

= 1/√2 sin x [since, π/4 = 1/√2]

= RHS

thus it is proved

hope you understand..m