Question

Find the value of sin (cos⁻¹ $\frac{3}{5}$)

Answer 1

Answer:

$sin(cos^{-1}\frac{3}{5} )=\frac{4}{5}$

Step-by-step explanation:

To find the value of

$sin(cos^{-1}\frac{3}{5} )$

as we know that cos inverse can be written in the form of sin inverse,so that at last sin cancels sine inverse.

$cos^{-1}x=sin^{-1}\sqrt{1-x^{2} } \\\\cos^{-1}\frac{3}{5} =sin^{-1}\sqrt{1-(\frac{3}{5})^{2} } \\\\=sin^{-1}\sqrt{1-(\frac{9}{25})} \\\\=sin^{-1}\sqrt{(\frac{25-9}{25}) } \\\\=sin^{-1}\sqrt{(\frac{16}{25}) } \\\\=sin^{-1}\frac{4}{5} \\\\\\so\\\\=> sin[sin^{-1}\frac{4}{5}]\\\\=\frac{4}{5}$

Answer 2

Answer:

$sin({cos}^{-1}\frac{3}{5})\\take \\\theta={cos}^{-1}\frac{3}{5}\\cos\theta=\frac{3}{5}\\{sin}^2\theta=1-{cos}^2\theta\\{sin}^2\theta=1-\frac{9}{25}\\{sin}^2\theta=\frac{16}{25}\\sin\theta=\frac{4}{5}\\Now,\\sin({cos}^{-1}\frac{3}{5})\\=sin\theta\\=\frac{4}{5}$