How i solve the tricky question no 4(3) of exercise 8.4 .Please solve this question of introduction of trigonometry of ncert class 10 .Give me the best solution of this optional question.Choose the correct option. Justify your choice.(iii) (sec A + tan A) (1 – sin A) = (A) sec A (B) sin A (C) cosec A (D) cos A.
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Choose the correct option. Justify your choice.(iii) (sec A + tan A) (1 – sin A) = (A) sec A (B) sin A (C) cosec A (D) cos A. Q.4(3)
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(D) is correct.
Justification:
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