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Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA
Most Upvoted Answer
Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA
Proof:
Given:
tanA/1+cotA + cotA/1-tanA = 1+secA cosecA
Proof:
Step 1: Simplifying LHS
tanA/1+cotA + cotA/1-tanA
= (tanA * cotA + cotA * 1) / (1 + cotA) (Finding a common denominator)
= (sinA/cosA * cosA/sinA + cosA/sinA) / (1 + cosA/sinA) (Applying trigonometric identities)
= (1 + cosA) / sinA (Simplifying)
Step 2: Simplifying RHS
1+secA cosecA
= 1 + (1/cosA) * (1/sinA) (Using trigonometric identities)
= 1 + (sinA * cosA) / (cosA * sinA) (Finding a common denominator)
= 1 + 1 (Simplifying)
= 2
Step 3: Comparing LHS and RHS
We have simplified LHS to (1 + cosA) / sinA and RHS to 2.
Since (1 + cosA) / sinA is not equal to 2, the given equation is incorrect.
Therefore, tanA/1+cotA + cotA/1-tanA is not equal to 1+secA cosecA.
Given:
tanA/1+cotA + cotA/1-tanA = 1+secA cosecA
Proof:
Step 1: Simplifying LHS
tanA/1+cotA + cotA/1-tanA
= (tanA * cotA + cotA * 1) / (1 + cotA) (Finding a common denominator)
= (sinA/cosA * cosA/sinA + cosA/sinA) / (1 + cosA/sinA) (Applying trigonometric identities)
= (1 + cosA) / sinA (Simplifying)
Step 2: Simplifying RHS
1+secA cosecA
= 1 + (1/cosA) * (1/sinA) (Using trigonometric identities)
= 1 + (sinA * cosA) / (cosA * sinA) (Finding a common denominator)
= 1 + 1 (Simplifying)
= 2
Step 3: Comparing LHS and RHS
We have simplified LHS to (1 + cosA) / sinA and RHS to 2.
Since (1 + cosA) / sinA is not equal to 2, the given equation is incorrect.
Therefore, tanA/1+cotA + cotA/1-tanA is not equal to 1+secA cosecA.
Community Answer
Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA
Hey just convert it into the term of sin in tan and cos and then solve
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Question Description
Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA for Class 10 2026 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA covers all topics & solutions for Class 10 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA.
Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA for Class 10 2026 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA covers all topics & solutions for Class 10 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that tanA/1+cotA. + CotA/1-tanA = 1+secAcosecA.
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