Question

Find a simplified expression for sin(tan ⁻¹(r/10)).

a)√ r²+100
b) r/√r²-100
c) √r²+100/r
d) √r²-100/r

Answer 1

The simplified expression for sin(tan ⁻¹(r/10)) is r/√(r²-100).

Step-by-step explanation:

To simplify the expression sin(tan ⁻¹(r/10)), we can use the trigonometric identity tan ⁻¹(x) = sin ⁻¹(x/√(1+x²)). Therefore, we can rewrite the expression as sin(sin ⁻¹(r/√(100+r²))), which simplifies to r/√(100+r²). Therefore, the correct option is b) r/√(r²-100).