Question

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

Answer 1

Please see the attachment

Answer 2

The value of $\theta[\tex] is [tex]\frac{n\pi}{2}$

Step-by-step explanation:

Given,

$sin\theta +cos\theta=1$ the  find the general value of \theta=?

∴ $sin\theta +cos\theta=1$

⇒ $(sin\theta +cos\theta)^{2} =1^{2}$ by squaring both sides.

⇒ $sin^{2} \theta+cos^{2} \theta+2.sin\theta.cos\theta=1$

⇒$1+sin2\theta=1$ (∵  $sin^{2} \theta+cos^{2} \theta=1$ )

⇒ $sin2\theta=0$

If  $sin2\theta=0$  then,

$2\theta=n\pi$

∴ $\theta=\frac{n\pi}{2}$ where $n∈Z[\tex]</p><p><strong>So, The value of [tex]\theta$ is $\frac{n\pi}{2}$