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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of l i m x → 0 l o g sin ⁡ 5 x + cos ⁡ 5 x tan ⁡ 3 x is equal to

Options

  1. A10 3
  2. B20 3
  3. C5 6
  4. D5 3

Correct answer

D. 5 3

Step-by-step solution

l i m x → 0 1 2 l o g 1 + sin ⁡ 10 x tan ⁡ 3 x ( as ,   1 + sin 10 x = ( sin 5 x + cos 5 x ) 2 ) = l i m x → 0 1 2 l o g ( 1 + s i n 10 x ) sin ⁡ 10 x ⋅ sin ⁡ 10 x 10 x ⋅ 3 x t a n 3 x ⋅ 10 x 3 x = 1 2 × 1 × 1 × 10 3 = 5 3

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