
Is sec the inverse of cos?
Answer
467.1k+ views
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 is an inverse function of and then we have . 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 .
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 . then the inverse of is denoted by and we have .
Now let us understand cos function. is a trigonometric ratio which gives the ratio of adjacent side and hypotenuse. Now hence is a function which takes the value of angle and then gives the corresponding cos value in the triangle.
Now similarly we have the trigonometric ratio . is a trigonometric ratio defined as the ratio of hypotenuse and adjacent side. Hence we have . Now note that sec is the inverse of cos but not the inverse function of cos. As if we have then . Hence the function sec is not the inverse function of cos.
Note: Now note that though the representation of an inverse function is we have . 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.
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
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
Now let us understand cos function.
Now similarly we have the trigonometric ratio
Note: Now note that though the representation of an inverse function is
Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹37,300 per year
Recently Updated Pages
Master Class 10 General Knowledge: Engaging Questions & Answers for Success

Master Class 10 Computer Science: Engaging Questions & Answers for Success

Master Class 10 Science: Engaging Questions & Answers for Success

Master Class 10 Social Science: Engaging Questions & Answers for Success

Master Class 10 Maths: Engaging Questions & Answers for Success

Master Class 10 English: Engaging Questions & Answers for Success

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE
