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.
