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Question
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
Solution
sin θ – cos θ = 0
sin θ = cos θ
`sinθ/cosθ` = 1
`\implies` tan θ = tan 45°
∴ θ = 45°
Now sin4 θ + cos4 θ = sin4 45° + cos4 45°
= `(1/sqrt(2))^4 + (1/sqrt(2))^4`
= `1/4 + 1/4`
= `2/4`
sin4 θ + cos4 θ = `1/2`
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