If \sin y=x \cos (a+y), then \frac{d x}{d y} is

Correct Answer is : cosacos2(a+y)

CBSE Class 12 Math 2022 Term I Solved Paper - Question 4

Question : 4 of 50

Marks: +1, -0

sin \;y=x \cos (a+y)

, then

\;{d x}/{d y}

Solution:

Explanation: Given,

sin \;y=x \cos (a+y)

⇒ \;\; x=\;{ sin \;y}/{\cos (a+y)}

Differentiating with respect to

y

, we get

\;{d x}/{d y}\;=\;{\cos (a+y) {d}/{d y}( sin \;y)- sin \;y {d}/{d y}\{\cos (a+y)\}}/{\cos ^2(a+y)}

⇒ \;{d x}/{d y}\;=\;{\cos (a+y) \cos y- sin \;y[- sin \;(a+y)]}/{\cos ^2(a+y)}

⇒ \;{d x}/{d y}\;=\;{\cos (a+y) \cos y+ sin \;y sin \;(a+y)}/{\cos ^2(a+y)}

⇒ \;{d x}/{d y}\;=\;{\cos [(a+y)-y]}/{\cos ^2(a+y)}

⇒ \;{d x}/{d y}\;=\;{\cos ^2 a}/{\cos ^2(a+y)}

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