The sin∠BPD is equal tocos∠CPN because ∠CPN = ∠NPD = a/2 and sin(90 - θ) = cosθ after using trigonometric identity.
What is an angle?
When two lines or rays converge at the same point, the measurement between them is called an "Angle."
We have a diagram showing PN is the perpendicular bisector of AB and is also the angle bisector of ∠CPD.
We know,
∠CPN = ∠NPD = a/2
From the figure,
∠NPD + ∠BPD = 90°
∠BPD = 90 - ∠NPD
∠BPD = 90 - a/2
sin(90 - θ) = cosθ
sin∠BPD = sin(90 - a/2) = cos(a/2) = cos∠CPN
sin∠BPD = cos∠CPN
Thus, the sin∠BPD is equal tocos∠CPN because ∠CPN = ∠NPD = a/2 and sin(90 - θ) = cosθ after using trigonometric identity.
Learn more about the angle here:
brainly.com/question/7116550
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