In a triangle ABC, sec A (sin B cos C + cos B sin C) equals:
tan A
Concept:
- sin (A + B) = sin A cos B + cos A sin B ___(1)
- The sum of the three angles of a triangle is 180°
- sin(180 - θ) = sin θ ___(2)
Calculation:
In triangle ABC, the sum of the angles = A + B + C = 180°
⇒ B + C = 180 - A ___(3)
Given, sec A (sin B cos C + cos B sin C)
⇒ sec A sin (B + C) ∵ Using {(1)}
⇒ sec A. sin (180 - A) ∵ Using {(2)}
⇒ sec A. sin A ∵ Using {(3)}
⇒ \({\sin A \over \cos A }\)
⇒ tan A
∴ The correct answer is option (3).
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