Question

Simplify and write the trigonometric expression in terms of sine and cosine: tan u cot u = 1 f ( u )

Answer 1

Finall Answer:

tan u cot u = 1 f(u) =
`sin^2(u) - cos^2(u)`

Step-by-step explanation:

The expression tan u cot u = 1 is transformed into f(u) =
`sin^2(u) - cos^2(u).`To understand this transformation, it's crucial to remember the fundamental trigonometric identities. Starting with tan u = sin u / cos u and cot u = cos u / sin u, multiplying these expressions results in 1. This simplifies further to f(u) =
`sin^2(u) - cos^2(u),` applying the Pythagorean identity tan u = 1/cot u, which is equal to
`sin^2(u) - cos^2(u).`

This simplification involves using the reciprocal identities of tangent and cotangent and Pythagorean identity for trigonometric functions. By substituting these identities, the equation becomes an expression in terms of sine and cosine squared, ultimately simplifying the initial product into the difference of their squares. This simplification aids in more straightforward calculations and problem-solving involving trigonometric equations.