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Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10?
Verified Answer
Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10?
Ans.
As you know
0≤sin(x)≤1,0≤x≤π
and hence
0≤sin(x)+2sin(2x)+3sin(3x)+4sin(4x)≤10
and we can have your equality only when all of the sin
's are equal to 1, i.e,
0≤sin(x)≤1,0≤x≤π
and hence
0≤sin(x)+2sin(2x)+3sin(3x)+4sin(4x)≤10
and we can have your equality only when all of the sin
's are equal to 1, i.e,
However, this is impossible because this leads to different values for x∈(0,π) at the same time. So the number of solutions is zero.
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Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10?
Solving the Trigonometric Equation sinA + 2sin2A + 3sin3A + 4sin4A = 10
- To solve the trigonometric equation sinA + 2sin2A + 3sin3A + 4sin4A = 10, we need to use trigonometric identities and properties to simplify the expression.
- We can start by expressing sin2A, sin3A, and sin4A in terms of sinA using double angle, triple angle, and quadruple angle identities.
- Apply the double angle identity: sin2A = 2sinAcosA, the triple angle identity: sin3A = 3sinA - 4sin^3(A), and the quadruple angle identity: sin4A = 4sinAcosA - 8sin^3(A)cosA.
- Substitute these expressions back into the original equation sinA + 2sin2A + 3sin3A + 4sin4A = 10 and simplify the equation.
- After simplifying, you should end up with a trigonometric equation involving only sinA.
- Solve the resulting trigonometric equation for sinA by using algebraic techniques such as factoring, setting terms equal to zero, or applying trigonometric identities.
- Once you find the value(s) of sinA, you can then determine the corresponding values of A by taking the inverse sine function.
- Verify your solution by substituting the values of A back into the original equation sinA + 2sin2A + 3sin3A + 4sin4A = 10 to ensure that it satisfies the equation.
- To solve the trigonometric equation sinA + 2sin2A + 3sin3A + 4sin4A = 10, we need to use trigonometric identities and properties to simplify the expression.
- We can start by expressing sin2A, sin3A, and sin4A in terms of sinA using double angle, triple angle, and quadruple angle identities.
- Apply the double angle identity: sin2A = 2sinAcosA, the triple angle identity: sin3A = 3sinA - 4sin^3(A), and the quadruple angle identity: sin4A = 4sinAcosA - 8sin^3(A)cosA.
- Substitute these expressions back into the original equation sinA + 2sin2A + 3sin3A + 4sin4A = 10 and simplify the equation.
- After simplifying, you should end up with a trigonometric equation involving only sinA.
- Solve the resulting trigonometric equation for sinA by using algebraic techniques such as factoring, setting terms equal to zero, or applying trigonometric identities.
- Once you find the value(s) of sinA, you can then determine the corresponding values of A by taking the inverse sine function.
- Verify your solution by substituting the values of A back into the original equation sinA + 2sin2A + 3sin3A + 4sin4A = 10 to ensure that it satisfies the equation.
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Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10?
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Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10?.
Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve: sinA + 2sin2A + 3sin3A + 4sin4A =10?.
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