How to find minimum maximum values quickly This is a guest article by Mr. Dipak Singh. if the math equationssigns are not clearly visible in your browser, then click me to download the PDF version of this article. Trig Identities. Min Max table. Ratta fication formulas. International Journal of Engineering Research and Applications IJERA is an open access online peer reviewed international journal that publishes research. An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Vb 6.0 Express Edition here. Easily share your publications and get. Banking Law And Practice Varshney Pdf Book' title='Banking Law And Practice Varshney Pdf Book' />The AM GM Logic. Find minimum value of 4 tan. Extra facts. SSC CGL 2. How To Install Neat Software Without Cd. Tier II Question. The least value of 2 sin. CGL2. 01. 2T1The maximum value of Sin x cos x  is The maximum value of 3 Sin x 4 Cos x  is Min Max values of  sin 4x 5 are. Minimum and maximum value of  Sin Sin x  is. Today well see how to find the maximum value greatest value or the minimum value least value of a trigonometric function without using differentiation. Take a pen and note book, keep doing the steps while reading this article. First Remember following identities Trig Identities. Already explained, click me. Min Max table. Min value. Max value. Can be written assin, sin 2, sin 9. Kerala k r l, historically known as Keralam, is an Indian state in South India on the Malabar Coast. It was formed on 1 November 1956 following the. Sin n 1cos, cos 4, cos 7 cos n 1 Cos n 1sin. Can be written as. Sin. 2 n 1cos. Cos. Sin Cos 1212 12 Sin Cos observe that in case of sin. Why does this happen Negative Signs inside out. Sin Sin Cos Cos Ratta fication formulasa sin b cos   a. Min. value of sin cos n n. The AM GM Logic. Let A ,B are any two numbers then,Arithmetic Mean AM A B 2 and. Geometric Mean GM A. BHence, A. M G. M   We can check it by putting any values of A and B Consider the following statement My age is greater than or equal to 2. What could you conclude about my age from this statement Answer My age can be anywhere between 2. Sweet 1. 6. Infact it can not be less than 2. Means, We can confidently say that my age is not less 2. Or in other words my minimum age is 2. Showing numerically, if Age 2. Similarly, If I say x 5. If, y 7. 7 minimum value of y 7. If, x y 1. 33 minimum value of x y 1. If, sin   1 minimum value of Sin 1 If, tan cot 2 minimum value of tan cot 2 Sometimes, we come across a special case of trigonometric identities like to find min. These identities have one thing in common i. These type of problems can be easily tackled by using the concept of. A. M G. MMeaning, Arithmetic mean is always greater than or equal to geometric mean. Activer La Mise En Veille Prolong E Windows 7'>Activer La Mise En Veille Prolong E Windows 7. For example Find minimum value of 4 tan. We know that tan. A. M G. M logic, we get. A. M of given equation 4 tan. G. M of given equation   4  tan. Now, we know that A. M G. MFrom equations 1 and 2 above we get, 4 tan. Multiplying both sides by 2  4 tan. Deriving a common conclusion Consider equation  a cos. As, A. M G. Ma cos. So, we can use 2 ab directly in these kind of problems. Summary While using A. M G. M logic Term should be like a T1 b T2 where  T1 1 T2. Positive sign in between terms is mandatory. Directly apply  2ab. RearrangeBreak terms if necessary priority should be given to direct use of identities   find terms eligible for A. M G. M logic if any, apply convert remaining identities, if any, to sine and cosines finally put known max., min. Extra facts The reciprocal of 0 is and vice versa. The reciprocal of 1 is 1 and 1 is 1. If a function has a maximum value its opposite has a minimum value. A function and its reciprocal have same sign. Keeping these tools not exhaustive in mind we can easily find Maximum or Minimum values easily. SSC CGL 2. 01. 2 Tier II Question. What is The minimum value of sin. Solution We know that sin. Therefore,sin. 2 cos. Using A. M G. M logic for tan. Because we know  maximum and minimum values of Sin, Cos P and by using simple identities we can convert all trigonometric functions into equation with Sine and Cosine. L. C. M 1 2   sin. Min. value of sin cos n n Ratta fication formula 4Apply them into eq. DThe least value of 2 sin. CGL2. 01. 2T11. 23. We can solve this question via two approaches. Approach 1. Break the equation and use identity no. BApproach 2convert equation into one identity ,either sin or cosfirst convert it into a sin equation 2 sin. Min. value of sin. As sin. 2 is preceded by a negative sign therefore we have to take max. Converting into a cos equation 2 sin. B The maximum value of Sin x cos x  is2. Applying Ratta fication formulae No. Sin x cos x 1. A The maximum value of 3 Sin x 4 Cos x  is 1. Solution Applying Ratta fication formulae No. Sin x 4 Cos x 3. B Min Max values of  sin 4x 5 are. Solution We know that, 1 Sin nx 1 1 Sin 4x 1. Adding 5 throughout, 4 Sin 4x 5 6. Therefore, the minimum value is 4 and maximum value is 6 correct answer D Minimum and maximum value of  Sin Sin x  is. Do not exist 1, 1. Sin 1 , Sin 1 Sin 1, Sin 1. We know that, 1 Sin nx 1 Sin 1 Sin x Sin 1  Sin 1 Sin x  Sin 1   Sin is same as Sin Therefore, Minimum value is Sin 1 and maximum is Sin 1 correct answer DThe key to success is Practice Practice PracticeDrop your problems in the comment box. For more articles on trigonometry and aptitude, visit mrunal. A method for obtaining digital signatures and public key cryptosystems.