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SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle?
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SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angl...
Proof that ABC is a Right Angled Isosceles Triangle
Given:
SinC cosC sin(2B C) - cos(2B C) = 2*(2^1/2)
To prove:
ABC is a right angled isosceles triangle
Proof:
- Given the trigonometric identity: sin(2B C) = 2sinC cosC and cos(2B C) = 1 - 2sin^2 C
- Substituting these identities into the given equation, we get:
sinC cosC * 2sinC cosC - (1 - 2sin^2 C) = 2*(2^1/2)
- Simplifying the equation, we get:
2sin^2 C cos^2 C - 1 + 2sin^2 C = 2*(2^1/2)
- Further simplifying, we get:
2sin^2 C (cos^2 C + 1) = 2*(2^1/2)
- Since cos^2 C + sin^2 C = 1 (from trigonometric identity), we have:
2sin^2 C = 2*(2^1/2)
- Simplifying, we get:
sin^2 C = 2^(3/2)
- Taking the square root of both sides, we get:
sin C = 2^(3/4)
Conclusion:
- Since sin C = 2^(3/4) > 1, it is not possible for a triangle to have a sine value greater than 1, which implies that the given equation is not valid.
- Therefore, the assumption that ABC is a right angled isosceles triangle based on the given equation is incorrect.
Given:
SinC cosC sin(2B C) - cos(2B C) = 2*(2^1/2)
To prove:
ABC is a right angled isosceles triangle
Proof:
- Given the trigonometric identity: sin(2B C) = 2sinC cosC and cos(2B C) = 1 - 2sin^2 C
- Substituting these identities into the given equation, we get:
sinC cosC * 2sinC cosC - (1 - 2sin^2 C) = 2*(2^1/2)
- Simplifying the equation, we get:
2sin^2 C cos^2 C - 1 + 2sin^2 C = 2*(2^1/2)
- Further simplifying, we get:
2sin^2 C (cos^2 C + 1) = 2*(2^1/2)
- Since cos^2 C + sin^2 C = 1 (from trigonometric identity), we have:
2sin^2 C = 2*(2^1/2)
- Simplifying, we get:
sin^2 C = 2^(3/2)
- Taking the square root of both sides, we get:
sin C = 2^(3/4)
Conclusion:
- Since sin C = 2^(3/4) > 1, it is not possible for a triangle to have a sine value greater than 1, which implies that the given equation is not valid.
- Therefore, the assumption that ABC is a right angled isosceles triangle based on the given equation is incorrect.
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SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle?
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SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle?.
SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for SinC cosC sin (2B C)-cos (2B C)=2*(2^1/2) Prove that ABC IS right angled isosceles triangle?.
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