Question

If sin theta+cos theta=1, then find the value of sin 2theta+cos 2theta

Answer 1

• The value of sin 2theta + cos 2theta is ±1.

Answer 2

The value of $\sin 2\theta+\cos 2\theta=\pm1$

Step-by-step explanation:

Given:

$\sin \theta+\cos \theta = 1$

Squaring both the sides, we get

$(\sin \theta+\cos \theta)^2 = 1^2\\\\\sin^2 \theta+\cos^2 \theta+2\sin \theta\cos \theta=1\\\\\textrm{We know,}\sin^2 \theta+\cos^2 \theta=1.So,\\\\1+2\sin \theta\cos \theta=1\\\\\textrm{We know,} 2\sin \theta\cos \theta=\sin2\theta\\\\1+\sin2\theta=1\\\\\sin2\theta=0$

Now, using the identity $\sin^2\theta+\cos^2\theta=1$

$\cos2\theta=\sqrt{1-\sin^22\theta}\\\\\cos2\theta=\sqrt{1-0}\\\\\cos2\theta=\pm1$

Now, $\sin 2\theta+\cos 2\theta=0+(\pm1)=\pm1$

Therefore, $\sin 2\theta+\cos 2\theta=\pm1$