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Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)?
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Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = ...
Proof:
Step 1: Simplify the given expression
- Start by simplifying the numerator and denominator separately:
(sinθ - cosθ + 1) / (sinθ + cosθ - 1)
Step 2: Use trigonometric identities
- Apply the trigonometric identities: secθ = 1/cosθ and tanθ = sinθ/cosθ
- Express the denominator in terms of sec and tan: (1/cosθ + sinθ/cosθ - 1)
Step 3: Simplify further
- Combine the terms in the denominator: (1 + sinθ - cosθ) / cosθ
- Simplify the expression to: (sinθ + 1 - cosθ) / cosθ
Step 4: Use trigonometric identities again
- Express sinθ and cosθ in terms of sec and tan: (secθ - tanθ + 1) / (secθ + tanθ - 1)
Step 5: Final step
- Since (secθ - tanθ + 1) / (secθ + tanθ - 1) is equal to 1/(secθ + tanθ), the given expression is proven to be equal to 1/(secθ + tanθ).
This completes the proof that (sinθ - cosθ + 1) / (sinθ + cosθ - 1) is equal to 1/(secθ + tanθ).
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Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)?
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Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)?.
Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = 1/(sec theta + tan theta)?.
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