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Prove that:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA?
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Prove that:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan...
Proof:
- Given expression: cosec A - sinA ÷ cosec A + sin A
Step 1: Simplify the left-hand side of the expression
- Apply the formula: cosec A = 1/sin A
- Substitute the values: 1/sin A - sin A ÷ 1/sin A + sin A
- Simplify the expression: (1 - sin^2 A) ÷ (1 + sin^2 A)
Step 2: Simplify the right-hand side of the expression
- Apply the formula: sec A = 1/cos A and tan A = sin A/cos A
- Substitute the values: (1/cos A) × (1/cos A) - (sin A/cos A) × (sin A/cos A) ÷ (1/cos A) × (1/cos A) + (sin A/cos A) × (sin A/cos A)
- Simplify the expression: (1/cos^2 A) - (sin^2 A/cos^2 A) ÷ (1/cos^2 A) + (sin^2 A/cos^2 A)
- Simplify further: (1 - sin^2 A) ÷ (1 + sin^2 A)
Step 3: Compare the simplified expressions
- We can see that the left-hand side of the expression is equal to the right-hand side after simplification
Therefore, cosec A - sinA ÷ cosec A + sin A = sec A × sec A - tan A × tan A ÷ sec A × sec A + tan A × tan A.
- Given expression: cosec A - sinA ÷ cosec A + sin A
Step 1: Simplify the left-hand side of the expression
- Apply the formula: cosec A = 1/sin A
- Substitute the values: 1/sin A - sin A ÷ 1/sin A + sin A
- Simplify the expression: (1 - sin^2 A) ÷ (1 + sin^2 A)
Step 2: Simplify the right-hand side of the expression
- Apply the formula: sec A = 1/cos A and tan A = sin A/cos A
- Substitute the values: (1/cos A) × (1/cos A) - (sin A/cos A) × (sin A/cos A) ÷ (1/cos A) × (1/cos A) + (sin A/cos A) × (sin A/cos A)
- Simplify the expression: (1/cos^2 A) - (sin^2 A/cos^2 A) ÷ (1/cos^2 A) + (sin^2 A/cos^2 A)
- Simplify further: (1 - sin^2 A) ÷ (1 + sin^2 A)
Step 3: Compare the simplified expressions
- We can see that the left-hand side of the expression is equal to the right-hand side after simplification
Therefore, cosec A - sinA ÷ cosec A + sin A = sec A × sec A - tan A × tan A ÷ sec A × sec A + tan A × tan A.
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Prove that:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA?
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Prove that:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA? 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:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA?.
Prove that:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA? 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:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that:- cosec A - sinA÷cosec A + sin A = secA × secA - tanA × tan A ÷ sec A × sec A + tan A×tanA?.
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