A=5 sec(A)/1-4sinA.sinA +cosecA/4cosA.cosA-1 find value
you seriously need some parentheses in there to make it clear what you want. As it stands, since multiplication is done before addition, you have
secA/1 - (4sinA)(sinA) + (cscA)/(4) * (cosA)(cosA) - 1
I seriously doubt that is what you wanted. Type it into the box at wolframalpha.com and keep inserting parentheses until it interprets correctly.
while you're at it, you can make A=5 and get your answer. Come on back if you can't figure out how woframalpha did it.
To find the value of A for the given expression, we can start by simplifying the expression using trigonometric identities.
Given expression: A = 5sec(A)/(1 - 4sinA.sinA) + cosecA/(4cosA.cosA - 1)
Step 1: Simplify sec(A) using the identity sec(A) = 1/cos(A). Substitute this in the expression:
A = 5(1/cos(A))/(1 - 4sinA.sinA) + cosecA/(4cosA.cosA - 1)
Step 2: Simplify cosecA using the identity cosecA = 1/sinA. Substitute this in the expression:
A = 5(1/cos(A))/(1 - 4sinA.sinA) + 1/sinA/(4cosA.cosA - 1)
Step 3: Simplify the denominators by multiplying them:
A = 5sinA/(cosA - 4sinA.sinA.cosA) + 1/(sinA(4cosA.cosA - 1))
Step 4: Simplify the expression using the identity cosA.sinA = 1/2*sin(2A):
A = 5sinA/(cosA - 2sin(2A)) + 1/(sinA(4cosA.cosA - 1))
Step 5: Simplify the denominators using the identity cosA.cosA = 1/2*(1 + cos(2A)):
A = 5sinA/(cosA - 2sin(2A)) + 1/(sinA*(2*(1 + cos(2A)) - 1))
Step 6: Combine the terms in the denominators:
A = 5sinA/(cosA - 2sin(2A)) + 1/(sinA*(2 + 2cos(2A) - 1))
Step 7: Simplify further:
A = 5sinA/(cosA - 2sin(2A)) + 1/(sinA*(1 + 2cos(2A)))
Now, to find the value of A, we need a specific value for either sinA, cosA, or cos(2A).
If you have a specific value for any of these trigonometric functions, substitute it into the expression above and calculate A.