Question

Write as an algebraic expression of x that does not involve trigonometric functions.

Answer 1

Given:

`\cos (\arcsin 3x+\arccos x)`
`\text{Let A= arcsin3x ; B= arccosx}`
`\sin A=3x\text{ ; }cosB=x`
`\cos (A+B)=\cos A\cos B-\sin A\sin B`
`\cos (A+B)=\cos A(x)-\sin B(3x)`
`\cos (A+B)=\sqrt[]{1-\sin^2A}(x)-\sqrt[]{1-\cos^2B}(3x)`
`\cos (A+B)=\sqrt[]{1-9x^2}(x)-\sqrt[]{1-x^2}(3x)`
`\cos (A+B)=x\sqrt[]{1-9x^2}-3x\sqrt[]{1-x^2}`

Therefore, 1st option is the correct answer.