Question

if sin - cos =0,then the value (sin⁴+cos⁴) is​

Answer 1

Answer:

2

Step-by-step explanation:

Answer 2

Answer:

The answer is $\frac{1}{2}$

Step-by-step explanation:

Given $\sin\theta-\cos\theta=0$

$\Rightarrow \sin\theta=\cos\theta\Rightarrow \frac{\sin\theta}{\cos\theta}=1\Rightarrow \tan\theta=1\therefore \theta=45^\circ$

Therefore,

$\sin^4\theta+\cos^4\theta=(\sin45^\circ)^4+(\cos45^\circ)^4\\=(\frac{1}{\sqrt 2})^4+(\frac{1}{\sqrt 2})^4=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$

( Since $\sin45^\circ=\cos45^\circ=\frac{1}{\sqrt 2}$ )