Question

tan(2cos⁻¹3/5) is.........,Select Proper option from the given options.
(a) 8/3
(b) 24/25
(c) 7/25
(d) - 24/7

Answer 1

Answer:

option (d) is correct

Step-by-step explanation:

$tan(2\:cos^{-1}\frac{3}{5})$

Take

$A=cos^{-1}\frac{3}{5}$

$cosA=\frac{3}{5}$

$\implies\:secA=\frac{5}{3}$

$tan^2A=sec^2A-1$

$tan^2A=\frac{25}{9}-1$

$tan^2A=\frac{25-9}{9}$

$tan^2A=\frac{16}{9}$

$tanA=\frac{4}{3}$

Now,

$tan(2\:cos^{-1}\frac{3}{5})$

$=tan2A$

$=\frac{2\:tanA}{1-tan^2A}$

$=\frac{2(\frac{4}{3})}{1-(\frac{4}{3})^2}$

$=\frac{\frac{8}{3}}{1-\frac{16}{9}}$

$=\frac{\frac{8}{3}}{\frac{9-16}{9}}$

$=\frac{\frac{8}{3}}{\frac{-7}{9}}$

$=\frac{8}{3}\times\:\frac{9}{-7}$

$=\frac{8}{1}\times\:\frac{3}{-7}$

$=\frac{-24}{7}$

$\implies\:\boxed{tan(2\:cos^{-1}\frac{3}{5})=\frac{-24}{7}}$