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sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A)
Most Upvoted Answer
sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A)
Explanation:
Step 1: Rewrite sin^3 A - cos^3 A as (sinA - cosA)(sin^2 A + sinA cosA + cos^2 A) using the identity a^3 - b^3 = (a-b)(a^2 + ab + b^2)
Step 2: Simplify sin^2 A + sinA cosA + cos^2 A as 1 - cos^2 A + sinA cosA + cos^2 A using the identity sin^2 A + cos^2 A = 1
Step 3: Simplify 1 - cos^2 A + sinA cosA + cos^2 A as sin^2 A + sinA cosA + cos^2 A - cos^2 A + cos^2 A
Step 4: Combine sin^2 A - cos^2 A and sinA cosA + cos^2 A - cos^2 A to get sin^2 A - cos^2 A + sinA cosA
Step 5: Factor sin^2 A - cos^2 A as (sinA + cosA)(sinA - cosA)
Step 6: Substitute sin^2 A - cos^2 A with (sinA + cosA)(sinA - cosA) in the expression sin^2 A - cos^2 A + sinA cosA to get (sinA + cosA)(sinA - cosA) + sinA cosA
Step 7: Simplify (sinA + cosA)(sinA - cosA) + sinA cosA to (sinA + cosA)^2 - sinA cosA using the identity (a+b)^2 = a^2 + 2ab + b^2
Step 8: Substitute (sinA + cosA)^2 with sin^2 A + cos^2 A + 2sinA cosA in the expression (sinA + cosA)^2 - sinA cosA to get sin^2 A + cos^2 A + 2sinA cosA - sinA cosA
Step 9: Simplify sin^2 A + cos^2 A + 2sinA cosA - sinA cosA as sin^2 A + cos^2 A + sinA cosA
Step 10: Substitute sin^2 A + cos^2 A with 1 in the expression sin^2 A + cos^2 A + sinA cosA to get 1 + sinA cosA
Step 11: Substitute 1 + sinA cosA with (1 - sin^2 A cos^2 A) + sinA cosA using the identity 1 - sin^2 A = cos^2 A and 1 - cos^2 A = sin^2 A
Step 12: Simplify (1 - sin^2 A cos^2 A) + sinA cosA as 1 - sin^2 A cos^2 A + sinA cosA
Step 13: Factor 1 - sin^2 A cos^2 A + sinA cosA
Step 1: Rewrite sin^3 A - cos^3 A as (sinA - cosA)(sin^2 A + sinA cosA + cos^2 A) using the identity a^3 - b^3 = (a-b)(a^2 + ab + b^2)
Step 2: Simplify sin^2 A + sinA cosA + cos^2 A as 1 - cos^2 A + sinA cosA + cos^2 A using the identity sin^2 A + cos^2 A = 1
Step 3: Simplify 1 - cos^2 A + sinA cosA + cos^2 A as sin^2 A + sinA cosA + cos^2 A - cos^2 A + cos^2 A
Step 4: Combine sin^2 A - cos^2 A and sinA cosA + cos^2 A - cos^2 A to get sin^2 A - cos^2 A + sinA cosA
Step 5: Factor sin^2 A - cos^2 A as (sinA + cosA)(sinA - cosA)
Step 6: Substitute sin^2 A - cos^2 A with (sinA + cosA)(sinA - cosA) in the expression sin^2 A - cos^2 A + sinA cosA to get (sinA + cosA)(sinA - cosA) + sinA cosA
Step 7: Simplify (sinA + cosA)(sinA - cosA) + sinA cosA to (sinA + cosA)^2 - sinA cosA using the identity (a+b)^2 = a^2 + 2ab + b^2
Step 8: Substitute (sinA + cosA)^2 with sin^2 A + cos^2 A + 2sinA cosA in the expression (sinA + cosA)^2 - sinA cosA to get sin^2 A + cos^2 A + 2sinA cosA - sinA cosA
Step 9: Simplify sin^2 A + cos^2 A + 2sinA cosA - sinA cosA as sin^2 A + cos^2 A + sinA cosA
Step 10: Substitute sin^2 A + cos^2 A with 1 in the expression sin^2 A + cos^2 A + sinA cosA to get 1 + sinA cosA
Step 11: Substitute 1 + sinA cosA with (1 - sin^2 A cos^2 A) + sinA cosA using the identity 1 - sin^2 A = cos^2 A and 1 - cos^2 A = sin^2 A
Step 12: Simplify (1 - sin^2 A cos^2 A) + sinA cosA as 1 - sin^2 A cos^2 A + sinA cosA
Step 13: Factor 1 - sin^2 A cos^2 A + sinA cosA
Community Answer
sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A)
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sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A)
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sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A) for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A) covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A).
sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A) for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A) covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for sin^3 A- cos^3 A = (sin^2 A-cos^2 A)(1-2sin^2 A cos^2A).
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