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Prove that: 2sin^(-1)(3/5)=tan^(-1)((24...

Prove that:` 2sin^(-1)(3/5)=tan^(-1)((24)/7)`

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To prove that \( 2 \sin^{-1} \left( \frac{3}{5} \right) = \tan^{-1} \left( \frac{24}{7} \right) \), we will follow these steps: ### Step 1: Use the Double Angle Formula for Inverse Sine We know that: \[ 2 \sin^{-1}(x) = \sin^{-1} \left( 2x \sqrt{1 - x^2} \right) \] Let \( x = \frac{3}{5} \). Then we can substitute this into the formula: ...
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