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Is sec the inverse of cos?

Answer
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Hint: Now we know that cos is nothing but the ratio of adjacent side and hypotenuse. Similarly sec is nothing but the ratio of hypotenuse and adjacent side. Now if f1 is an inverse function of f and f(x)=y then we have f1(y)=x . Hence we will check sec is the inverse function of cos.

Complete step by step solution:
Now first let us understand the concept of functions and inverse functions.
Now a function can be imagined as a machine which takes an input to a unique output.
Hence let us say we have a value x. then the function takes the value and given an output y. Hence we have f(x)=y .
Now let us understand the concept of inverse function. Inverse function of a function is the function which reverses the role of the actual function.
Hence if we have f as a function where f(x)=y . then the inverse of f is denoted by f1 and we have f1(y)=x .
Now let us understand cos function. cosis a trigonometric ratio which gives the ratio of adjacent side and hypotenuse. Now hence cosθ is a function which takes the value of angle θ and then gives the corresponding cos value in the triangle.
Now similarly we have the trigonometric ratio sec . sec is a trigonometric ratio defined as the ratio of hypotenuse and adjacent side. Hence we have secθ=1cosθ . Now note that sec is the inverse of cos but not the inverse function of cos. As if we have cos0=1 then sec10 . Hence the function sec is not the inverse function of cos.

Note: Now note that though the representation of an inverse function is f1(x) we have 1f(x)f1(x) . Hence not to be confused between the two terms. Also note that the inverse of all functions does not exist; the function needs to satisfy certain criteria for the inverse function to exist. The criteria is the function needs to be one-one and onto.

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