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Mathematics

The value of :

cosec 40° cos 50° + sin 50° sec 40° is:

  1. 1

  2. 2

  3. 3

  4. 0

Trigonometric Identities

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Answer

Given:

cosec 40° cos 50° + sin 50° sec 40°

= cosec 40° cos (90° - 40°) + sin (90° - 40°) sec 40°

= cosec 40° sin 40° + cos 40° sec 40°

= 1sin 40°×sin 40°+cos 40°×1cos 40°\dfrac{1}{\text{sin 40°}} \times \text{sin 40°} + \text{cos 40°} \times \dfrac{1}{\text{cos 40°}}

= 1 + 1

= 2

Hence, option 2 is the correct option.

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