sec^2xcotx-cotx=tanx
(1/cos)^2 times (1/tan)-(1/tan)=tan
(1/cos^2) times (-2/tan)=tan
(-2/cos^2tan)times tan=tan(tan)
sq. root of (-2/cos^2)= sq. root of (tan^2)
sq. root of (2i)/cos=tan
I'm not sure if I did this right. If I didn't, can you show me the correct steps?
Thanks, I appreciate it.
sec^2(x)cot(x) - cot(x) = tan(x)
Convert everything to sine and cosine using the identity tan(x) = sin(x)/cos(x).
cos^-2(x)(cos(x)/sin(x)) - cos(x)/sin(x) = sin(x)/cos(x)
1/( cos(x)sin(x) ) - cos(x)/sin(x) = sin(x)/cos(x)
Note: it is important to write sin(x) as opposed to sin, because you may find equations that include different parameters -- sin(x) and sin(2x), for example.
tan7.50
To solve the equation sec^2(x)cot(x) - cot(x) = tan(x), we can follow these steps:
Step 1: Simplify the left side of the equation.
Using the trigonometric identities: sec^2(x) = 1/cos^2(x) and cot(x) = 1/tan(x), we can rewrite the equation as:
(1/cos^2(x))(1/tan(x)) - (1/tan(x)) = tan(x).
Step 2: Combine the fractions on the left side of the equation.
We can factor out 1/tan(x) from the first two terms:
(1/cos^2(x))(1/tan(x)) - (1/tan(x)) = (1/tan(x))(1/cos^2(x) - 1).
Step 3: Simplify the expression inside the parentheses.
Using the identity: 1 - cos^2(x) = sin^2(x), we can rewrite the expression as:
(1/tan(x))(1 - cos^2(x)) = (1/tan(x))(sin^2(x)).
Step 4: Simplify further.
Using the identity: sin^2(x) = 1 - cos^2(x), we can rewrite the expression as:
(1/tan(x))(1 - cos^2(x)) = (1/tan(x))(1 - 1 + cos^2(x)).
Simplifying, we have:
(1/tan(x))(1 - cos^2(x)) = (1/tan(x))(cos^2(x)).
Step 5: Cancel out common factors.
Since we have (1/tan(x)) on both sides of the equation, we can cancel it out:
1 - cos^2(x) = cos^2(x).
Step 6: Simplify further.
Rearranging the terms, we have:
cos^2(x) + cos^2(x) = 1.
Combining like terms, we get:
2cos^2(x) = 1.
Step 7: Solve for cos^2(x)
Divide both sides by 2:
cos^2(x) = 1/2.
Step 8: Take the square root.
Taking the square root of both sides, we have:
cos(x) = ±(1/√2).
Step 9: Find the corresponding angle values.
Since cos(x) = adjacent/hypotenuse, we need to determine the values of x where the ratio of the adjacent and hypotenuse is ±(1/√2).
By looking at the unit circle, we can find that the angles corresponding to cos(x) = ±(1/√2) are x = π/4 and x = 7π/4.
Step 10: Final solution.
The values of x that satisfy the given equation are x = π/4 + nπ and x = 7π/4 + nπ, where n is an integer.