ProofHard3 marks
Prove that: (cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1
Topic: Trigonometric identities
Previous-year question practice database
Answer
Exam answer
Left-hand side = (cosecθ−sinθ)(secθ−cosθ)(tanθ+cotθ)
= [(1−sin²θ)/sinθ] [(1−cos²θ)/cosθ] [(sin²θ+cos²θ)/(sinθcosθ)]
= [cos²θ/sinθ][sin²θ/cosθ][1/(sinθcosθ)] = 1.
Hence proved.
Explanation
Convert to sine/cosine and use 1−sin²θ=cos²θ, 1−cos²θ=sin²θ and sin²θ+cos²θ=1.
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