Let ABC be a triangle such as 2cosA+3sinB=4 and 3cosB+2sinA=3 Prove that the angle C is right.


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Question Number 117825 by snipers237 last updated on 13/Oct/20

$L e t A B C b e a t r i a n g l e s u c h a s$ $2 c o s A + 3 s i n B = 4 a n d 3 c o s B + 2 s i n A = 3$ $P r o v e t h a t t h e a n g l e C i s r i g h t .$
	Answered by john santu last updated on 13/Oct/20

	$2 \cos A + 3 \sin B = 4$ $2 \sin A + 3 \cos B = 3$ $\Rightarrow 4 \cos^{2} A + 12 \cos A \sin B + 9 \sin^{2} B = 16$ $\Rightarrow 4 \sin^{2} A + 12 \sin A \cos B + 9 \cos^{2} B = 9$ $(1) + (2)$ $\Rightarrow 13 + 12 \sin (A + B) = 25$ $\Rightarrow 12 \sin (A + B) = 12$ $\Rightarrow \sin (A + B) = 1 \Rightarrow A + B = 90 °$ $A + B + C = 180 ° \Rightarrow 90 ° + C = 180 °$ $t h e n C = 90 °$
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