Question

How do you express sin x + cos x in terms of sine only?

Answer 1

`\sin x + √(1-\sin^2x)`

Explanation:

Given: sin x + cos x

To change the given trigonometry expression in term of sine only.

Trigonometry identity:-

• 
  `\sin^2x+\cos^2x=1`
• 
  `\cos x=√(1-\sin^2x)`

Expression:
`\sin x+\cos x`

We get rid of cos x from expression and write as sine form.

Expression:
`\sin x + √(1-\sin^2x)`
`\because \cos x=√(1-\sin^2x)`

Hence, The final expression is only sine function.