The Value Of Sinh Ix A Isin X B Sin Ix C Isin X D Isin Class 11 Maths CBSE

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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsThe value of $ \sinh (ix) = $ a. $ i\sin x $ b. $ \sin (ix) $ c. $ - i\sin x $ d. $ i\sin ix $ AnswerVerified560.4k+ viewsHint: Here we will use the formula for hyperbolic function and the formula of sine function expressed in exponential form. Since the standard formula is expressed in terms of “x”, we will convert the form in “ix” form. Then will simplify the equation for the resultant answer. Complete step-by-step answer:Using the identity for hyperbolic function – $ \sinh x = \dfrac{{{e^x} - {e^{ - x}}}}{2} $ Here, the given function is with respect to therefore convert “x” to “ix” form Therefore, the above equation can be expressed as – $ \Rightarrow \sinh (ix) = \dfrac{{{e^{ix}} - {e^{ - ix}}}}{2} $ .... (A)Also, $ {e^{ix}} = \cos x + i\sin x $ Place the above value in equation (A) $ \Rightarrow \sinh (ix) = \dfrac{{(\cos x + i\sin x) - (\cos ( - x) + i\sin ( - x))}}{2} $ Now, use the properties of sines and cosines and apply accordingly. The odd and even trigonometric functions states that - $ \sin ( - \theta ) = - \sin \theta \\ \cos ( - \theta ) = \cos \theta \; $ $ \Rightarrow \sinh (ix) = \dfrac{{(\cos x + i\sin x) - (\cos x - i\sin x)}}{2} $ Now, open the brackets and simplify. Remember when there is a negative sign outside the bracket, all the terms inside the bracket changes. Positive term changes to negative and negative becomes positive. $ \Rightarrow \sinh (ix) = \dfrac{{\cos x + i\sin x - \cos x + i\sin x}}{2} $ Make the pair of like terms and simplify – $ \Rightarrow \sinh (ix) = \dfrac{{\underline {\cos x - \cos x} + \underline {i\sin x + i\sin x} }}{2} $ Like terms with equal value and opposite signs cancel each other. And add like terms with positive terms. $ \Rightarrow \sinh (ix) = \dfrac{{2i\sin x}}{2} $ Common multiple from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator. $ \Rightarrow \sinh (ix) = i\sin x $ So, the correct answer is “Option A”.Note: Always remember the standard hyperbolic formula for the trigonometric function and the exponential form of the trigonometric function. Remember the standard formula properly as the further solution depends on it. Be clear with the odd and even trigonometric function. Cosine is an even function whereas sine is an odd function. Recently Updated PagesMaster Class 11 English: Engaging Questions & Answers for SuccessMaster Class 11 Biology: Engaging Questions & Answers for SuccessMaster Class 11 Physics: Engaging Questions & Answers for SuccessMaster Class 11 Maths: Engaging Questions & Answers for SuccessMaster Class 11 Accountancy: Engaging Questions & Answers for SuccessClass 11 Question and Answer - Your Ultimate Solutions GuideMaster Class 11 English: Engaging Questions & Answers for SuccessMaster Class 11 Biology: Engaging Questions & Answers for SuccessMaster Class 11 Physics: Engaging Questions & Answers for SuccessMaster Class 11 Maths: Engaging Questions & Answers for SuccessMaster Class 11 Accountancy: Engaging Questions & Answers for SuccessClass 11 Question and Answer - Your Ultimate Solutions Guide

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