If A + B + C = 180°and cos B. cos C = cos A, then what is the value o

1.	If A + B + C = 180°and cos B. cos C = cos A, then what is the value of tan B. tan C? (A) – 2 (B) – 1 (C) 2 (D) 1
Answer» (C) 2 Given A + B + C = 180 \(\downarrow\) cos B cos C = cos A …. (1) ∴ cos(B + C) = – cos A cos A – sin B sin C = – cos A sin B sin C = 2 cos A …. (2) (2)/(1) = tan B tan C = 2

If A + B + C = 180°and cos B. cos C = cos A, then what is the value of tan B. tan C? (A) – 2 (B) – 1 (C) 2 (D) 1

Answer»

(C) 2

Given A + B + C = 180 \(\downarrow\) cos B cos C = cos A …. (1)

∴ cos(B + C) = – cos A

cos A – sin B sin C = – cos A

sin B sin C = 2 cos A …. (2)

(2)/(1) = tan B tan C = 2

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