Question

sinA + cosA / sinA - cosA = 5/4 find tan2A +1 / tan2A - 1 = ?​

Answer 1

sinA+cosAsinA−cosA=54

(sinA+cosAsinA−cosA)2=(54)2

sin2A+2sinAcosA+cos2Asin2A−2sinAcosA+cos2A=2516

1+sin2A1−sin2A=2516

16(1+sin2A)=25(1−sin2A)

41sin2A=9

sin2A=941

sinA+cosAsinA−cosA=54

(sinA+cosA)(sinA+cosA)(sinA−cosA)(sinA+cosA)=54

sin2A+2sinAcosA+cos2Asin2A−cos2A=54

1+sin2A−cos2A=54

cos2A=−45(1+sin2A)=−45(1+941)

cos2A=−4041

tan2A=sin2Acos2A=−940

tan2A+1tan2A−1=−940+1−940−1=−9+40−9–40=−3149

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