Choose the correct option. Justify your choice. (sec A + tan A) (1 – sin A) =? (A) sec A (B) sin A (C) cosec A (D) cos A

Answer: (D) cos A

We know that,

  • sec A= 1/cos A
  • tan A = sin A / cos A

Now, substitute the above values in the given problem, we get

(secA + tanA) (1 – sinA)

= (1/cos A + sin A/cos A) (1 – sinA)

= (1+sin A/cos A) (1 – sinA)

= (1 – sin2A)/cos A

= cos2A/cos A

= cos A

Therefore, (secA + tanA) (1 – sinA) = cos A

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