Question

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

Answer 1

Answer:

$\sin x + \sqrt{1-\sin^2x}$

Step-by-step explanation:

Given: sin x + cos x

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

Trigonometry identity:-

• $\sin^2x+\cos^2x=1$
• $\cos x=\sqrt{1-\sin^2x}$

Expression: $\sin x+\cos x$

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

Expression: $\sin x + \sqrt{1-\sin^2x}$        $\because \cos x=\sqrt{1-\sin^2x}$

Hence, The final expression is only sine function.