In the following figure, the area of the pedal triangle is - Options: A . &nbsp 12R2.sin A.sin B.sin C B . &nbsp12R2.sin 2A.sin 2B.sin 2C C . &nbsp 12R2.cos A.cos B.cos C D . &nbsp None of these

Answer: Option B : B Since, area of a triangle = 1 2 (product of the sides) × sine of the included angle) = 1 2 R sin 2 B ⋅ sin ( 180 ° − 2 A ) = 1 2 R 2 sin 2 A ⋅ sin 2 B ⋅ sin 2 C

In the following figure, the area of the pedal triangle is -

Question

In the following figure, the area of the pedal triangle is -

Options:

A . 12R2.sin A.sin B.sin C

B . 12R2.sin 2A.sin 2B.sin 2C

C . 12R2.cos A.cos B.cos C

D . None of these

Answer: Option B
:
B
Since, area of a triangle

= \frac{1}{2} (product of the sides) \times sine of the included angle)

= \frac{1}{2} R sin 2 B \cdot sin (180 ° - 2 A)

= \frac{1}{2} R^{2} sin 2 A \cdot sin 2 B \cdot sin 2 C

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