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Introduction to Trigonometry
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16/06/2021 11:06 am
Topic starter
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
1 Answer
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16/06/2021 11:07 am
Correct option: (D) cos A
Explanation:
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