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By geometrical interpretation, prove tha...

By geometrical interpretation, prove that
`tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)`.

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AI Generated Solution

To prove the identity \( \tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta} \) using geometrical interpretation, we can follow these steps: ### Step 1: Draw a Right Triangle for Each Angle 1. Draw a right triangle for angle \( \alpha \) with: - Opposite side = \( a \) - Adjacent side = \( b \) - Therefore, \( \tan \alpha = \frac{a}{b} \). ...
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Knowledge Check

  • (1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=

    A
    `tan^2alphatan^2beta`
    B
    `sec^2alphasec^2beta`
    C
    `tan^2alphacot^2beta`
    D
    `sec^2alphacos^2beta`
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