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trigonometric properties from unit circle: secant, cosecant, tangent and cotangent

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Why is cos(theta + alpha) = cos(theta).cos(alpha) - sin(theta).sin(alpha)
and sin(theta + alpha) = sin(theta).cos(alpha) + cos(theta).sin(alpha)?
why is sin(90-theta) = cos(theta)?
more videos on Trigonometry --
and sin(theta + alpha) = sin(theta).cos(alpha) + cos(theta).sin(alpha)?
why is sin(90-theta) = cos(theta)?
more videos on Trigonometry --
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