The answer is cos A .
cos A = 1/ (sec A)
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Since sin(a)=opposite/hypotenuse, the reciprocal function is that function which is equal to hypotenuse/opposite. This is "cosecant", or csc(a). The reciprocal of sin(a) is csc(a). I will solve all your math problems. Check my profile for more info.
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.
Cosecant
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.