If sin θ – cos θ = 0, then the value of (sin ^{ 4 } θ + cos ^{ 4 } θ) is
(A) 1
(B) 3/4
(C) 1/2
(D) 1/4
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Last updated at April 16, 2024 by Teachoo
Question 16 If sin θ – cos θ = 0, then the value of (sin4 θ + cos4 θ) is (A) 1 (B) 3/4 (C) 1/2 (D) 1/4 Given sin θ – cos θ = 0 sin θ = cos θ This can only happen if θ = 45° Now, sin4 θ + cos4 θ = sin4 45° + cos4 45° = (1/√2)^4+(1/√2)^4 = 2 × (𝟏/√𝟐)^𝟒 = 2 × [(1/√2)^2 ]^2 = 2 × [1/2]^2 = 2 × 1/4 = 𝟏/𝟐 So, the correct answer is (C)