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If cosA cos2A = 1 then the value of sin2A sin4A is?
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If cosA cos2A = 1 then the value of sin2A sin4A is?
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If cosA cos2A = 1 then the value of sin2A sin4A is?
Cosine Double Angle Formula:
The cosine double angle formula states that cos(2A) = 2cos^2(A) - 1.
Given:
cos(A) * cos(2A) = 1
Using the Cosine Double Angle Formula:
cos(2A) = 2cos^2(A) - 1
Substituting the given equation:
cos(A) * (2cos^2(A) - 1) = 1
Simplifying the equation:
2cos^3(A) - cos(A) = 1
Factoring out cos(A):
cos(A)(2cos^2(A) - 1) = 1
Dividing both sides by 2cos^2(A) - 1:
cos(A) = 1 / (2cos^2(A) - 1)
Using the Pythagorean Identity:
cos^2(A) + sin^2(A) = 1
Solving for sin^2(A):
sin^2(A) = 1 - cos^2(A)
Substituting into the equation:
cos(A) = 1 / (2(1 - sin^2(A)) - 1)
Simplifying the equation:
cos(A) = 1 / (2 - 2sin^2(A) - 1)
cos(A) = 1 / (1 - 2sin^2(A))
Cross-multiplying:
cos(A)(1 - 2sin^2(A)) = 1
Distributing:
cos(A) - 2sin^2(A)cos(A) = 1
Factoring out common term:
cos(A)(1 - 2sin^2(A)) = 1
Dividing both sides by cos(A):
1 - 2sin^2(A) = 1 / cos(A)
Using the Pythagorean Identity:
1 - 2sin^2(A) = sec(A)
Substituting into the equation:
sec(A) = 1 / cos(A)
Using the Reciprocal Identity:
1 / cos(A) = sec(A)
Substituting sec(A) back into the equation:
1 - 2sin^2(A) = sec(A)
Adding 2sin^2(A) to both sides:
1 = sec(A) + 2sin^2(A)
Substituting the given equation:
1 = cos(A) * cos(2A) + 2sin^2(A)
Using the Identity:
cos(2A) = 2cos^2(A) - 1
Substituting into the equation:
1 = cos(A) * (2cos^2(A) - 1) + 2sin^2(A)
Expanding the equation:
1 = 2cos^3(A) - cos(A) + 2sin^2(A)
Simplifying the equation:
2cos^3(A) + 2sin^
The cosine double angle formula states that cos(2A) = 2cos^2(A) - 1.
Given:
cos(A) * cos(2A) = 1
Using the Cosine Double Angle Formula:
cos(2A) = 2cos^2(A) - 1
Substituting the given equation:
cos(A) * (2cos^2(A) - 1) = 1
Simplifying the equation:
2cos^3(A) - cos(A) = 1
Factoring out cos(A):
cos(A)(2cos^2(A) - 1) = 1
Dividing both sides by 2cos^2(A) - 1:
cos(A) = 1 / (2cos^2(A) - 1)
Using the Pythagorean Identity:
cos^2(A) + sin^2(A) = 1
Solving for sin^2(A):
sin^2(A) = 1 - cos^2(A)
Substituting into the equation:
cos(A) = 1 / (2(1 - sin^2(A)) - 1)
Simplifying the equation:
cos(A) = 1 / (2 - 2sin^2(A) - 1)
cos(A) = 1 / (1 - 2sin^2(A))
Cross-multiplying:
cos(A)(1 - 2sin^2(A)) = 1
Distributing:
cos(A) - 2sin^2(A)cos(A) = 1
Factoring out common term:
cos(A)(1 - 2sin^2(A)) = 1
Dividing both sides by cos(A):
1 - 2sin^2(A) = 1 / cos(A)
Using the Pythagorean Identity:
1 - 2sin^2(A) = sec(A)
Substituting into the equation:
sec(A) = 1 / cos(A)
Using the Reciprocal Identity:
1 / cos(A) = sec(A)
Substituting sec(A) back into the equation:
1 - 2sin^2(A) = sec(A)
Adding 2sin^2(A) to both sides:
1 = sec(A) + 2sin^2(A)
Substituting the given equation:
1 = cos(A) * cos(2A) + 2sin^2(A)
Using the Identity:
cos(2A) = 2cos^2(A) - 1
Substituting into the equation:
1 = cos(A) * (2cos^2(A) - 1) + 2sin^2(A)
Expanding the equation:
1 = 2cos^3(A) - cos(A) + 2sin^2(A)
Simplifying the equation:
2cos^3(A) + 2sin^
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If cosA cos2A = 1 then the value of sin2A sin4A is?
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If cosA cos2A = 1 then the value of sin2A sin4A is? 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 If cosA cos2A = 1 then the value of sin2A sin4A is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosA cos2A = 1 then the value of sin2A sin4A is?.
If cosA cos2A = 1 then the value of sin2A sin4A is? 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 If cosA cos2A = 1 then the value of sin2A sin4A is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cosA cos2A = 1 then the value of sin2A sin4A is?.
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