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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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