Proof that cos theta is equal to 8 upon 17:

Given: Secant theta minus tan theta is equal to 4.

To prove: cos theta is equal to 8 upon 17.

Proof:

We know that secant theta is equal to 1/cos theta and tan theta is equal to sin theta/cos theta. Therefore,

sec theta - tan theta = 1/cos theta - sin theta/cos theta

= (1 - sin theta) / cos theta

Given that sec theta - tan theta = 4, we can write:

(1 - sin theta) / cos theta = 4

Multiplying both sides by cos theta, we get:

1 - sin theta = 4cos theta

Squaring both sides, we get:

1 + sin^2 theta - 2sin theta = 16cos^2 theta

Since 1 + sin^2 theta = cos^2 theta, we can substitute to get:

cos^2 theta - 2sin theta = 16cos^2 theta

Simplifying, we get:

15cos^2 theta = 2sin theta

Using the identity sin^2 theta + cos^2 theta = 1, we can substitute sin^2 theta with 1 - cos^2 theta to get:

15cos^2 theta = 2(1 - cos^2 theta)

Simplifying, we get:

17cos^2 theta = 2

Dividing both sides by 17, we get:

cos^2 theta = 2/17

Taking the square root of both sides, we get:

cos theta = sqrt(2/17)

Simplifying, we get:

cos theta = 8/17

Therefore, cos theta is equal to 8 upon 17.

Sec* - Tan * = 4
(1/cos)-(sin/cos)=4

Cos=(1-sin)/4 . ..