Verify the Identity sin(x)sec(x)cot(x)=1

Problem

sin(x)*sec(x)*cot(x)=1

Solution

1. Express the trigonometric functions in terms of sine and cosine using the reciprocal and quotient identities.

2. Substitute sec(x)=1/cos(x) and cot(x)=cos(x)/sin(x) into the left side of the equation.

sin(x)⋅1/cos(x)⋅cos(x)/sin(x)

3. Simplify the expression by canceling the common factors in the numerator and the denominator.

(sin(x)⋅cos(x))/(cos(x)⋅sin(x))

4. Reduce the fraction to its simplest form.

1

Final Answer

sin(x)*sec(x)*cot(x)=1

Want more problems? Check here!