Question

19. Represent tan(sin^-1 x) in terms of x only.​

Answer 1

Step-by-step explanation:

We have,

$\tt{tan \left(sin^{ - 1} (x) \right)}$

$\tt{ = \dfrac{sin \left(sin^{ - 1} (x) \right)}{cos \left(sin^{ - 1} (x) \right)}}$

$\tt{ = \dfrac{sin \left(sin^{ - 1} (x) \right)}{ \sqrt{1 - sin^{2} \left(sin^{ - 1} (x) \right)}}}$

$\tt{ = \dfrac{x}{ \sqrt{1 - x ^{2} }}}$