If sin θ - cos θ = 0, then find the value of sin4 θ + cos4 θ.

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Q) If sin θ – cos θ = 0, then find the value of sin⁴ θ + cos⁴ θ.

Ans: Since sin θ – cos θ = 0

$\therefore$ sin θ = cos θ

hence tan θ = 1 and θ = 45⁰

and hence sin 45⁰ = cos 45⁰ = $\frac{1}{\sqrt2}$

sin⁴ θ + cos⁴ θ

= sin⁴ 45 + cos⁴ 45

= $(\frac{1}{\sqrt2})^4$ + $(\frac{1}{\sqrt2})^4$

= $(\frac{1}{4})$ + $(\frac{1}{4})$

= $(\frac{1}{2})$

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