Trigonometry is the study of the measure of the triangles, and these measures can be calculated using various trigonometric formulas. In trigonometry, there are formulas relating sides and angles of a triangle, area of a triangle and other estimations of a triangle. There are 6 basic trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. These 6 functions define trigonometry and the trigonometric formulas are based on these functions. Trigonometric identities are also trigonometric formulas which relate one function to the other function.
Example 1: If P = sin(x) * sec(x) and Q = cos(x) * cosec(x), then what is the value of P * Q?
Given: P = sin(x) * sec(x)
Q = cos(x) * cosec(x)
Now, P = sin(x) * sec(x) ==> P = sin(x) * 1/cos(x)
This gives, P = tan(x)
Now, Q = cos(x) * cosec(x) ==> Q = cos(x) * 1/(sin(x)
This gives, Q = cot(x)
So therefore, P * Q = tan(x) * cot(x) = 1 (Since they are reciprocal of each other)
Example 2: Simplify the give trigonometric expression, tan(x) + 1/cot(x).
Given: tan(x) + 1/cot(x)
In order to simplify the expression, we can re-write cot(x) in terms of tan(x).
Now, 1/cot(x) = tan(x) because ‘tangent’ and ‘cotangent’ of an angle are reciprocals of each other.
Now this gives: tan(x) + 1/cot(x) ==> tan(x) + tan(x) = 2tan(x)
Hence therefore, the given trigonometric expression, tan(x) + 1/cot(x) can be simplified to 2tan(x).