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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
Let ABC be a triangle such as 2cosA+3sinB=4 and 3cosB+2sinA=3 Prove that the angle C is right.
LetABCbeatrianglesuchas2cosA+3sinB=4and3cosB+2sinA=3ProvethattheangleCisright.
Answered by john santu last updated on 13/Oct/20
2cos A+3sin B=4 2sin A+3cos B=3 ⇒4cos^2 A+12cos Asin B+9sin^2 B=16 ⇒4sin^2 A+12sin Acos B+9cos^2 B=9 (1)+(2) ⇒13+12sin (A+B)=25 ⇒12sin (A+B)=12 ⇒sin (A+B)=1 ⇒A+B=90° A+B+C=180°⇒90°+C=180° then C = 90°
2cosA+3sinB=42sinA+3cosB=3⇒4cos2A+12cosAsinB+9sin2B=16⇒4sin2A+12sinAcosB+9cos2B=9(1)+(2)⇒13+12sin(A+B)=25⇒12sin(A+B)=12⇒sin(A+B)=1⇒A+B=90°A+B+C=180°⇒90°+C=180°thenC=90°

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