If cotA=3/4find the value of 2sinA-3cosA ÷2sinA - 3cosA.
make a sketch of the triangle
cotA = 3/4 ---> x=3, y=4
by Pythagoras r = 5
now we can find all possible trig ratios
sinA = 4/5
cosA = 3/5
Once you establish the proper order of operation of your expression, just sub in the values
e.g. is it
2sinA-3cosA ÷(2sinA - 3cosA)
or
2sinA-(3cosA) ÷(2sinA) - 3cosA
or
2sinA-(3cosA ÷2)sinA - 3cosA , the way it would be according to BEDMAS
To find the value of the expression (2sinA - 3cosA) ÷ (2sinA - 3cosA), we can simplify it by first substituting the given value cotA = 3/4.
Using the trigonometric identity cotA = 1/tanA, we can rewrite cotA as cosA/sinA:
cosA/sinA = 3/4
Next, we can cross-multiply to eliminate the denominators:
4cosA = 3sinA
Now, let's square both sides of the equation to eliminate the trigonometric functions:
(4cosA)^2 = (3sinA)^2
16cos^2(A) = 9sin^2(A)
Using the Pythagorean identity sin^2(A) + cos^2(A) = 1, we can substitute cos^2(A) as 1 - sin^2(A) in the equation above:
16(1 - sin^2(A)) = 9sin^2(A)
Now, let's simplify the equation:
16 - 16sin^2(A) = 9sin^2(A)
Rearranging the terms, we get:
25sin^2(A) = 16
Taking the square root of both sides, we have:
sin(A) = ±√(16/25) = ±4/5
Since sin(A) is positive in the first and second quadrants, we take the positive value:
sin(A) = 4/5
Now, we can substitute this value into the original expression:
(2sinA - 3cosA) ÷ (2sinA - 3cosA) = (2 * 4/5 - 3 * cosA) ÷ (2 * 4/5 - 3 * cosA)
Simplifying further:
(8/5 - 3cosA) ÷ (8/5 - 3cosA)
Since the numerator and denominator are the same, the expression simplifies to:
1
Therefore, the value of (2sinA - 3cosA) ÷ (2sinA - 3cosA) is 1.