A2sec2A -b2tan2A =c2.Prove that sin2A = c2 - a2 / c2 - b2
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a²sec²A-b²tan²A=c²
or, a²sec²A-b²(sec²A-1)=c²
or, a²sec²A-b²sec²A+b²=c²
or, sec²A(a²-b²)=c²-b²
or, sec²A=c²-b²/a²-b²
∴, cos²A=1/sec²A=1/(c²-b²/a²-b²)=a²-b²/c²-b²
∵, sin²A+cos²A=1
or, sin²A=1-cos²A
or, sin²A=1-(a²-b²/c²-b²)
or, sin²A=(c²-b²-a²+b²)/(c²-b²)
or, sin²A=c²-a²/c²-b² (Proved)
or, a²sec²A-b²(sec²A-1)=c²
or, a²sec²A-b²sec²A+b²=c²
or, sec²A(a²-b²)=c²-b²
or, sec²A=c²-b²/a²-b²
∴, cos²A=1/sec²A=1/(c²-b²/a²-b²)=a²-b²/c²-b²
∵, sin²A+cos²A=1
or, sin²A=1-cos²A
or, sin²A=1-(a²-b²/c²-b²)
or, sin²A=(c²-b²-a²+b²)/(c²-b²)
or, sin²A=c²-a²/c²-b² (Proved)
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