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1. if A,B,C are interior angles of AABC, show that cosec2 Btc-tana = 1.AnA 1 |
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Answer» A+B+C= 180DIVIDED BY 2 BOTH SIDEA+B+C/2=180/2B+C/2+A/2=90B+C/2=90-A/2cosec^2B+C/2-tan^2A/2cosec^2(90-A/2)- tan^A/2sec^2A/2-tan^2A/2let A/2= psec^2p-tan^2p=1 A+B+C=180; B+C=180-A___(1); cosecx^2( b+c/2)-tan^2(a/2); Substitutiing 1 in cosecx^2(b+c/2) = cosecx^2(180/2-a/2)-tan^2(a/2)= cosex^2(90-a/2)-tan^2(a/2); identity cosecx(90-x)=secx;=sec^2(a/2)-tan^2(a/2); identity secx^2- tanx^2=1;sec^2(a/2)-tan^2(a/2)=1 gfsf Girish fyh rheostats Sharma Diana |
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