the expression the quantity secant of x plus 1 end quantity over tangent of x was simplified with the following steps: step 1: secant x over tangent x plus 1 over tangent x step 2: the quantity 1 over cosine x end quantity over tangent x plus 1 over tangent x step 3: the quantity 1 over cosine x end quantity over the quantity sine x over cosine x end quantity plus cosine x over sine x step 4: 1 over sine x plus cosine x over sine x step 5: cosecant x plus cosine x over sine x step 6: cosecant x plus cotangent x which identity/formula was used to simplify from step 4 to step 5?

The connections between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It is founded on the principles of right triangles, that are right angles. We can use trigonometry to calculate the lengths of the sides of a right triangle given the lengths of some or all of the other sides. It also enables us to determine the angle's size in a right triangle given its side tangent. In various disciplines, such as engineering, physics, and astronomy, trigonometry is utilised to solve issues involving triangles and the characteristics of circles. It is also used in navigation and surveying to estimate distances and angles between sites.

How to solve?

This identity allows us to rewrite the expression 1/sine x as cosecant x. Therefore, in step 4 we have 1/sine x + cosine x/sine x, and in step 5 we have cosecant x + cosine x/sine x = cosecant x + cotangent x.

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