Question

Solution please! explain clearly​

Answer 1

Answer:

  2

Step-by-step explanation:

For some angle "a", the sine and cosine are related by ...

  sin(a) = cos(π/2 -a)

That is,

  sin(7π/16) = cos(π/16)

  sin(5π/16) = cos(3π/16)

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Then your sum becomes ...

  sum = sin(π/16)² +sin(3π/16)² +cos(3π/16)² +cos(π/16)²

If we let α = π/16 and β = 3π/16, this can be written as ...

  sum = (sin(α)² +cos(α)²) +(sin(β)² +cos(β)²)

  sum = 1 + 1

  sum = 2

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The identity sin(α)² +cos(α)² = 1 is sometimes called the Pythagorean identity.