If-a-cos-A-b-cos-B-in-a-ABC-then-C-is-

Question Number 54970 by Tip Top last updated on 15/Feb/19

If a \cos A = b \cos B in a △ A B C,

then ∠ C is

Answered by $@ty@m last updated on 15/Feb/19

G i v e n

\frac{a}{b} = \frac{\cos B}{\cos A} \dots (1)

W e k n o w t h a t

\frac{a}{b} = \frac{\sin A}{\sin B} \dots (2)

f r o m (1) a n d (2)

\frac{\cos B}{\cos A} = \frac{\sin A}{\sin B}

\sin A \cos A = \sin B \cos B

\sin 2 A = \sin 2 B

\Rightarrow A = B o r 2 A = π - 2 B

f r o m 2 A = π - 2 B

w e g e t

A = \frac{π}{2} - B

\Rightarrow A + B = \frac{π}{2}

\Rightarrow C = \frac{π}{2}

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