Practicing Success
If tan A + sec A = K, then what is the value of sin A ? |
$\frac{2k}{k^2+1}$ $\frac{K^2-1}{2K}$ $\frac{K^2+1}{K^2-1}$ $\frac{K^2-1}{K^2+1}$ |
$\frac{K^2-1}{K^2+1}$ |
tan A + sec A = K ----(1) sec A - tan A = \(\frac{1}{K}\) ----(2) Adding to 1 & 2 2 secA = K + \(\frac{1}{K}\) = \(\frac{ K2 + 1}{K}\) secA = \(\frac{ K2 + 1}{2K}\) Subtracting 1 & 2 2 tanA = K - \(\frac{1}{K}\) = \(\frac{ K2 - 1}{K}\) tanA = \(\frac{ K2 - 1}{2K}\) \(\frac{tanA}{secA}\) = \(\frac{ K2 - 1}{2K}\) × \(\frac{ 2K}{K2 + 1}\) sinA = \(\frac{ K2 - 1}{K2 + 1}\) |