tan(sin^-1(5/6)-cos^-1(1/5)

can someone help me please????

I assume you mean on the sin and cosine ^-1 actually you mean the invsin or invcos, or as Many of us, we call those

ARCSIN
ARCCCOS

meaning the angle whose sin/cosine is ..

Tan(arcsin (5/6)-ARCcos(1/5))

The easy way is to do this on a calculator.

So, the hard way.

Tan(A-B)= (tanA-TanB)/(1+tanA*tanB) check that formula. Now substituter a and b.

On each angle, draw it, you can figure the tan exactly. For instance on arcsin5/6, you know the opposite side is 5, the hypotensuse is 5, so the adjacent6 side is sqrt (36-25)=sqrt11 so Tan of that angle is 5/sqrt11

I answered the same type of question here

http://www.jiskha.com/display.cgi?id=1334539340

Just change the numbers

To find the value of tan(sin^-1(5/6) - cos^-1(1/5)), we need to understand the steps involved in evaluating this expression.

Step 1: Identify the inverse trigonometric functions
In the given expression, sin^-1(5/6) represents the inverse sine function, and cos^-1(1/5) represents the inverse cosine function.

Step 2: Evaluate the inverse sine function
sin^-1(5/6) means finding an angle whose sine is 5/6.
To evaluate this, we can use the fact that sin^-1(x) returns the angle between -π/2 and π/2 whose sine is x.
So, we need to find an angle (let's call it angle A) whose sine is 5/6.

Step 3: Solve for angle A
Angle A lies in between -π/2 and π/2, so its sine value will be positive.
Using a calculator, we find that sin^-1(5/6) is approximately 0.9273 radians (or about 53.13 degrees).

Step 4: Evaluate the inverse cosine function
cos^-1(1/5) means finding an angle whose cosine is 1/5.
To evaluate this, we can use the fact that cos^-1(x) returns the angle between 0 and π whose cosine is x.
So, we need to find an angle (let's call it angle B) whose cosine is 1/5.

Step 5: Solve for angle B
Angle B lies between 0 and π, so its cosine value will be positive.
Using a calculator, we find that cos^-1(1/5) is approximately 1.3694 radians (or about 78.69 degrees).

Step 6: Calculate the difference of the angles
Now that we have the values of angle A (0.9273 radians) and angle B (1.3694 radians), we can subtract angle B from angle A:
angle_A - angle_B = 0.9273 - 1.3694 = -0.4421 radians (or about -25.37 degrees).

Step 7: Evaluate the tangent of the difference of the angles
Finally, we can find the tangent of the difference of the angles by using the tangent function:
tan(-0.4421) ≈ -0.4747.

Therefore, tan(sin^-1(5/6) - cos^-1(1/5)) is approximately -0.4747.