ProofHard4 marks
Prove the following identity : (sin² θ - 1)(tan² θ + 1) + 1 = 0
Topic: Trigonometric identities
Previous-year question practice database
Answer
Exam answer
Left-hand side = (sin²θ−1)(tan²θ+1)+1 = (−cos²θ)(sec²θ)+1 = −1+1 = 0 = Right-hand side.
Explanation
Use sin²θ−1=−cos²θ and tan²θ+1=sec²θ.
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