ProofHard4 marks
Factorize: sin³ θ + cos³ θ Hence, prove the following identity: (sin³ θ + cos³ θ) / (sin θ + cos θ) + sin θ cos θ = 1
Topic: Remainder and factor theorem
Previous-year question practice database
Answer
Exam answer
sin³θ+cos³θ=(sinθ+cosθ)(1−sinθcosθ). Therefore (sin³θ+cos³θ)/(sinθ+cosθ)+sinθcosθ = 1.
Explanation
Use a³+b³=(a+b)(a²−ab+b²) and sin²θ+cos²θ=1.
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