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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 64 of 72
Marks: +1, -0
sin⁡(x+a)cos⁡x\frac{\sin(x+a)}{\cos x}
Solution:  
Let f (x) = sin⁡(x+a)cos⁡x\frac{\sin(x+a)}{\cos x} ... (i)
Differentiating (i) with respect to x, we get
ddx\frac{d}{dx} (f (x)) =
cos⁡x(sin⁡(x+a))′−sin⁡(x+a)(cos⁡x)′(cos⁡x)2\frac{\cos x (\sin(x+a))' - \sin(x+a) (\cos x)'}{(\cos x)^2}
=
cos⁡xcos⁡(x+a)−sin⁡(x+a)(−sin⁡x)(cos⁡x)2\frac{\cos x \cos(x+a) - \sin(x+a)(-\sin x)}{(\cos x)^2}
=
cos⁡xcos⁡(x+a)+sin⁡(x−a)⋅sin⁡x(cos⁡x)2\frac{\cos x \cos(x+a) + \sin(x-a) \cdot \sin x}{(\cos x)^2}
= cos⁡[x+a−x](cos⁡x)2\frac{\cos[x+a-x]}{(\cos x)^2}
= cos⁡a(cos⁡x)2\frac{\cos a}{(\cos x)^2}
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