reciprocal identity cosθ=
1/secθ
The reciprocal identity for cosine (cos) is 1/secant (sec) or cosθ = 1/secθ.
In a right triangle, cosθ is defined as the ratio of the adjacent side to the hypotenuse. Alternatively, secθ is defined as the ratio of the hypotenuse to the adjacent side.
Therefore, we can get the reciprocal identity by taking the reciprocal (i.e., flipping the fraction) of the cosine function.
Mathematically, if we let θ be an angle in a right triangle, we can express the cosine and secant functions as:
cosθ = adjacent/hypotenuse
secθ = hypotenuse/adjacent
Taking the reciprocal of both sides of the first equation, we get:
1/cosθ = hypotenuse/adjacent = secθ
Thus, we have the reciprocal identity for cosine as cosθ = 1/secθ.
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