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If y = sin (log cos x) then what is the value of 

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  1. cos (log (cos x)).tan x
  2. sin (log (cos x)).tan x
  3. -cos (log (cos x)).tan x
  4. -cos (log (sin x)).tan x

Answer (Detailed Solution Below)

Option 3 : -cos (log (cos x)).tan x
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Detailed Solution

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Concept:

Differentiation Formulas

 = cos x 

 = - sin x

Trigonometry Formula

 

Calculation:

Given:y = sin (log cos x)

Differentiation with respect to x

 = 

= cos (log (cos x)). 

= cos (log (cos x)).  

= cos (log (cos x)).  .(- sin x)

= - cos (log (cos x)). 

= - cos (log (cos x)).tan x​​

 = - cos (log (cos x)).tan x

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