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If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is?
Most Upvoted Answer
If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles,...
Given Information:
Find: cos x-y/2
Solution:
Step 1: Use the formula for cos(x-y) to find cos(x-y):
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(x-y) = (3/5)(4/5) + sqrt(1-(3/5)^2) sqrt(1-(4/5)^2)
cos(x-y) = 12/25 + 3/5 * 4/5
cos(x-y) = 27/25
Step 2: Use the half-angle formula for cosine to find cos((x-y)/2):
cos((x-y)/2) = ± sqrt((1+cos(x-y))/2)
Note that we must take the positive square root because x and y are acute angles.
cos((x-y)/2) = sqrt((1+27/25)/2)
cos((x-y)/2) = sqrt(52/50)
cos((x-y)/2) = sqrt(26)/5
Answer: Therefore, cos x-y/2 = sqrt(26)/5
- cos x = 3/5
- cos y = 4/5
- x and y are positive acute angles
Find: cos x-y/2
Solution:
Step 1: Use the formula for cos(x-y) to find cos(x-y):
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(x-y) = (3/5)(4/5) + sqrt(1-(3/5)^2) sqrt(1-(4/5)^2)
cos(x-y) = 12/25 + 3/5 * 4/5
cos(x-y) = 27/25
Step 2: Use the half-angle formula for cosine to find cos((x-y)/2):
cos((x-y)/2) = ± sqrt((1+cos(x-y))/2)
Note that we must take the positive square root because x and y are acute angles.
cos((x-y)/2) = sqrt((1+27/25)/2)
cos((x-y)/2) = sqrt(52/50)
cos((x-y)/2) = sqrt(26)/5
Answer: Therefore, cos x-y/2 = sqrt(26)/5
Community Answer
If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles,...
Given
cosx=3/5
cosy=4/5
cosx-y/2 =3/5-4/5 /2
=-1/5/2
=-1/10
cosx=3/5
cosy=4/5
cosx-y/2 =3/5-4/5 /2
=-1/5/2
=-1/10
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If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is?
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If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is?.
If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If cos x= 3/5 and cos y = 4/5,where x and y are positive acute angles, then cos x-y/2 is?.
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