The answer is cos A .
cos A = 1/ (sec A)
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Sin(A) = Opposite/Hypotenuse Its reciprotcal is 1/Sin(A) = Cosecant(A) = Csc(A) = Hypotenuse / Opposite. Similarly Cos(A) = Adjacent/Hypotenuse Its reciprotcal is 1/Cos(A) = Secant(A) = Sec(A) = Hypotenuse / Adjacent Tan(A) = Opposite/Adjacent Its reciprotcal is 1/Tan(A) = Cotangent(A) = Cot(A) = Adjacent / Opposite.
Sine Its reciprocal is Cosecant Algebraically Sin ; Reciprocal is '1/ Sin' known as 'Cosecant(Csc)'. Similarly Cos(Cosine) ; 1/ Cos (Secant(Sec)) Tan(Tangent) ; 1/ Tan ( Cotangent(Cot)).
Trigonometry includes 12 baisic functions. Sine, Cosine, and Tangent are the three most baisic. Each of those functions has a reciprocal. Cosine's reciprocal is Secant, Sine reciprocal is Cosecant, and Tangent's reciprocal is Cotangent. Each of those six functions has an inverse funcion called Inverse Sine, Cos etc... or Arcsine, Arcosine, Arcsecant, etc.... The shorthand for each function is sin, caos, tan, sec, csc, cot. The inverses have a -1 notation like sin-1.
The reciprocal of the tangent is the cotangent, or cot. We might write 1/tan = cot.
The cotangent function is the reciprocal of the tangent function, so cot(115 degrees) is equivalent to 1/tan(115 degrees). Since tan(115 degrees) is equivalent to -tan(65 degrees) due to the periodicity of the tangent function, cot(115 degrees) simplifies to -tan(65 degrees), which corresponds to option A.