Find the exact value of the expression.
tan( sin−1 (2/3)− cos−1(1/7))

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

Let .

With some restriction on this means:

We need to find .

is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

Subtract 4/9 on both sides:

Take the square root of both sides:

The cosine value is positive because is a number between and because that is the restriction on sine inverse.

So we have .

This means that .

Multiplying numerator and denominator by 3 gives us:

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

Let's continue on to letting .

Let's go ahead and say what the restrictions on are.

is a number in between 0 and .

So anyways implies .

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of .

Subtract 1/49 on both sides:

Take the square root of both sides:

So since is a number between and , then sine of this value is positive.

This implies:

So .

Multiplying both top and bottom by 7 gives:

.

Let's put everything back into the first mentioned identity.

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

answer:

what is your question that you ask

step-by-step explanation:

bull

step-by-step explanation: