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If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2?
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If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n ...
Given: Angle mcos a - mdina = p
To prove: mcosa- - nsina = - ( m n - p )2
Proof:
Step 1: Rearrange the given equation
mcosa - p = mdina
Step 2: Square both sides of the equation
(mcosa - p)2 = m2d2ina
m2cos2a - 2mpcosa + p2 = m2d2in2a
Step 3: Rearrange the terms
m2cos2a - m2d2in2a = 2mpcosa - p2
(m2 - m2d2)cos2a = 2mpcosa - p2
(m2/m2d2 - 1)cos2a = 2mpcosa - p2
Step 4: Simplify the expression
cos2a = (2mpcosa - p2)/(m2/m2d2 - 1)
cos2a = [(2mpcosa - p2)(m2d2)]/(m2 - m2d2)
cos2a = [(2mpcosa)(m2d2) - p2(m2d2)]/(m2 - m2d2)
cos2a = [(2mpcosa)(n) - p2(n)]/(m - n)
cos2a = (2mpcosa - p2)/(m - n)
Step 5: Use trigonometric identities to simplify the expression
cos2a - sin2a = (2mpcosa - p2)/(m - n) - (m - n)/(m - n)
cos2a - sin2a = (2mpcosa - p2 - m2 + n2)/(m - n)
cos2a - sin2a = (n2 - m2 + 2mpcosa - p2)/(m - n)
cos2a - sin2a = (n - m)2 - (mpcosa - p)2/(m - n)2
cos2a - sin2a = -(mpcosa - p)2/(m - n)2 + (n - m)2
cos2a - sin2a = -(m n - p)2
Step 6: Divide both sides by -1
mcosa- - nsina = (m n - p)2
Therefore, the given equation mcosa - nsina = -(m n - p)2 is proved.
To prove: mcosa- - nsina = - ( m n - p )2
Proof:
Step 1: Rearrange the given equation
mcosa - p = mdina
Step 2: Square both sides of the equation
(mcosa - p)2 = m2d2ina
m2cos2a - 2mpcosa + p2 = m2d2in2a
Step 3: Rearrange the terms
m2cos2a - m2d2in2a = 2mpcosa - p2
(m2 - m2d2)cos2a = 2mpcosa - p2
(m2/m2d2 - 1)cos2a = 2mpcosa - p2
Step 4: Simplify the expression
cos2a = (2mpcosa - p2)/(m2/m2d2 - 1)
cos2a = [(2mpcosa - p2)(m2d2)]/(m2 - m2d2)
cos2a = [(2mpcosa)(m2d2) - p2(m2d2)]/(m2 - m2d2)
cos2a = [(2mpcosa)(n) - p2(n)]/(m - n)
cos2a = (2mpcosa - p2)/(m - n)
Step 5: Use trigonometric identities to simplify the expression
cos2a - sin2a = (2mpcosa - p2)/(m - n) - (m - n)/(m - n)
cos2a - sin2a = (2mpcosa - p2 - m2 + n2)/(m - n)
cos2a - sin2a = (n2 - m2 + 2mpcosa - p2)/(m - n)
cos2a - sin2a = (n - m)2 - (mpcosa - p)2/(m - n)2
cos2a - sin2a = -(mpcosa - p)2/(m - n)2 + (n - m)2
cos2a - sin2a = -(m n - p)2
Step 6: Divide both sides by -1
mcosa- - nsina = (m n - p)2
Therefore, the given equation mcosa - nsina = -(m n - p)2 is proved.
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If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2?
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If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2?.
If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If angle mcos a - mdina = p then prove that mcosa- - nsina = - ( m n - p )2?.
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