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Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ?
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Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ?
Proof of 1-cos a sin a / sin a cos a-1 = sin a / cos a
Step 1: Simplify the left-hand side
To simplify the left-hand side of the equation, we can use the identity:
1 - cos a = sin^2 a / (1 + cos a)
Substituting this into the left-hand side, we get:
(sin^2 a / (1 + cos a)) * (sin a / cos a) / (sin a cos a - 1)
Next, we can simplify the denominator by using the identity:
sin a cos a - 1 = -1 + sin^2 a / cos^2 a
Substituting this into the left-hand side, we get:
(sin^2 a / (1 + cos a)) * (sin a / cos a) / (-1 + sin^2 a / cos^2 a)
Now, we can simplify the numerator by using the identity:
sin a = sin^2 a / cos a
Substituting this into the left-hand side, we get:
(sin^2 a / (1 + cos a)) * (sin^2 a / cos^2 a) / (-1 + sin^2 a / cos^2 a)
Simplifying the fraction, we get:
sin^4 a / (cos^2 a - sin^2 a - cos a + 1)
Step 2: Simplify the right-hand side
To simplify the right-hand side of the equation, we can use the identity:
sin a / cos a = tan a
Substituting this into the right-hand side, we get:
tan a
Step 3: Equate the left-hand side and right-hand side
Now, we can equate the left-hand side and right-hand side of the equation:
sin^4 a / (cos^2 a - sin^2 a - cos a + 1) = tan a
Step 4: Simplify the equation
We can simplify the equation by multiplying both sides by (cos^2 a - sin^2 a - cos a + 1):
sin^4 a = tan a * (cos^2 a - sin^2 a - cos a + 1)
Expanding the right-hand side, we get:
sin^4 a = cos^2 a tan a - sin^2 a tan a - cos a tan a + tan a
Using the identity:
tan a = sin a / cos a
We can simplify the equation to:
sin^4 a = cos a sin a - sin^3 a - cos a sin a + sin a
Simplifying further, we get:
sin^4 a = sin
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Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ?
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Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ?
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Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ? 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 Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ?.
Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ? 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 Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Prove that 1-cos a sin a /sin a cos a-1=1 sin a /cos a ?.
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