Question

evaluate cos(arcsin(3/5) - arccos(3/5))

Answer 1

Use the double angle formula for cosine and definition of inverses. So,

Answer 2

\[\cos (\sin^{-1}\frac{3}{5}-\cos^{-1}\frac{3}{5})\]\[=\cos (\sin^{-1}\frac{3}{5}) \cos(\cos^{-1}\frac{3}{5})+\sin(\sin^{-1}\frac{3}{5})\sin(\cos^{-1}\frac{3}{5})\]

Answer 3

\[=\sqrt{1-\sin^2(\sin^{-1}\frac{3}{5}})\frac{3}{5}+\frac{3}{5}\sqrt{1-\sin^2(\sin^{-1}\frac{3}{5})}\]

Answer 4

\[=\sqrt{1-\left( \frac{3}{5} \right)^2}\frac{3}{5}+\frac{3}{5}\sqrt{1-\left( \frac{3}{5} \right)^2}\]\[=2.\frac{3}{5}\sqrt{\frac{16}{25}}=\frac{6}{5}\frac{4}{5}=\frac{24}{25}\]

Answer 5

Fin.

Answer 6

thank you

Answer 7

No probs. Become a fan ;)

Answer 8

ok i will

Answer 9

Thanks