Question

sin[cot^-1{cos(tan^-1)}]

Answer 1

$\huge\mathsf{Hoy \ !!}$

$\large\mathsf{\underline{ \ Given \ : \ }}$

$\large\mathsf{sin \ [ \ {cot}^{-1} \ \{ \ cos \ ( \ {tan}^{-1} \ ) \ \} \ ]}$

$\large\mathsf{sin \ [ {\dfrac{1}{cot}} \ \{ \ cos \ ( \ {\dfrac{1}{tan}} \ ) \ \} \ ]}$

$\large\mathsf{Now,}$

$\large{\boxed{\mathsf{\red{Using \ some \ formulas}}}}$

${\large{\boxed{\mathsf{\red{{\dfrac{1}{cot}} \ = \ tan}}}}}$

$\large\therefore$

$\large\mathsf{sin \ [ \ tan \ \{ \ cos \ ( \ {\dfrac{1}{tan}} \ ) \ \} \ ]}$

$\large\mathsf{sin × tan × cos × {\dfrac{1}{tan}}}$

$\large\mathsf{sin × {\cancel{tan}} × cos × {\dfrac{1}{{\cancel{tan}}}}}$

$\large\mathsf{sin × cos}$

$\large\mathsf\red{sin.cos}$

$<b><i>$
^^"