Question

If y = a sin x + b cos x, prove that $straight y squared plus open parentheses dy over dx close parentheses squared equals straight a squared plus straight b squared$ .

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Solution

Here space space straight y equals straight a space sin space straight x plus straight b space cos space straight x space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis therefore space dy over dx equals straight a space cos space straight x minus straight b space sin space straight x space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis Squaring space and space adding space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get comma space space space space space space space space space straight y squared plus open parentheses dy over dx close parentheses squared equals straight a squared left parenthesis sin squared straight x plus cos squared space straight x right parenthesis plus straight b squared left parenthesis cos squared straight x plus sin squared straight x right parenthesis therefore space space space space space straight y squared plus open parentheses dy over dx close parentheses squared equals straight a squared left parenthesis 1 right parenthesis plus straight b squared left parenthesis 1 right parenthesis therefore space space space space space straight y squared plus open parentheses dy over dx close parentheses squared equals straight a squared plus straight b squared

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Continuity And Differentiability

If y = a sin x + b cos x, prove that $straight y squared plus open parentheses dy over dx close parentheses squared equals straight a squared plus straight b squared$ .

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Continuity And Differentiability

If y = a sin x + b cos x, prove that .

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If y = a sin x + b cos x, prove that $straight y squared plus open parentheses dy over dx close parentheses squared equals straight a squared plus straight b squared$ .