Question

24. If sin theta - cos theta = 0, then the value of sin^4 theta + cos^4 theta will be
​

Answer 1

$\rm \dfrac{1}{2}$

Step-by-step explanation:

$\rm \sin θ - \cos θ =0$

$\rm \sin θ = \cos θ$

$\rm \sin θ = \sin (90-θ)$

$\rm θ = 90-θ$

$\rm 2 θ =90$

$\rm θ = 45^{\circ}$

$\rm \sin ^4 \theta + \cos ^4 θ$

$\rm \sin ^4 (45^{\circ}) + \cos ^4 (45^{\circ})$

$\rm \bigg( \dfrac{1}{\sqrt{2}} \bigg) ^{4} +\bigg( \dfrac{1}{\sqrt{2}} \bigg) ^{4}$

$\rm = \dfrac{1}{4} + \dfrac{1}{4}$

$\rm = \dfrac{1}{2}$

Answer 2

hope it helps you

mark as brainest and follow