ProofHard3 marks
Prove that : (sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ
Topic: Trigonometric identities
Previous-year question practice database
Answer
Exam answer
Left-hand side = (secθ−cosθ)(cosecθ−sinθ) = [sin²θ/cosθ]·[cos²θ/sinθ] = sinθ cosθ = Right-hand side.
Explanation
secθ−cosθ=(1−cos²θ)/cosθ=sin²θ/cosθ; similarly cosecθ−sinθ=cos²θ/sinθ.
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