Question

If $\sin \theta -\cos \theta =0,$ find the value of ${\sec }^4\theta +cose{c}^4\theta$.

Answer 1

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

$\Rightarrow \sin \theta =\cos \theta$

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

Now, ${\sec }^4\theta +cose{c}^4\theta$

$={\sec }^4{45}^{\circ }+cose{c}^4{5}^{\circ }$

$={\left(\sqrt{2}\right)}^4+{\left(\sqrt{2}\right)}^4$

$=4+4=8$