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7If cot 0 = , evaluate:(1 + sin 0) (1 - sin o)(1 + cos 0) (1 - cos 0) |
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Answer» cotA= 7/8b/p= 7/8b/7=p/8= k(let)b= 7kp= 8kh^2=p^+b^2 = (8k)^2+(7k)^2 = 64j^2+49k^2 = 113k^2h= k√113sinA= p/h= 8k/k√113 = 8/√113(1-sinA)(1-sinA)=1-sin^2A{(a+b)(a-b)=a^2-b^2)=1-64/113=113-64/113= 49/113cos^2A= b^2/h^2 = 49k^2/113k^2=49/113(1+cosA)(1-cosA)=1-cos^2A= 1-49/113= 113-49/113= 64/113(!+sinA)(1-sinA)/(1+cosA)(1-cosA)= 49/113/64/113= 49/64 cotx=7/8; (hypo)^2=64+49=113; ( hypo)=V113; sinx=8/V113, cosx=7/V113; (1+8/V113)(1-8/V113)/ (1+7/V113)(1-7/V113)= (1+sinx)(1-sinx)/ (1+cosx)(1- cosx)= (1-sinx^2)/1-cosx^2)= (1-64/113)/(1-49/113)= (113-49/113) /(113-64/113)= (113-49)/(113-64)=64/49=8/7 cot¢= 7/8(i) (1+sin¢)(1-sin¢)/(1+cos¢)(1-cos¢)=(1-sin^2¢)/(1-cos^2¢)=cos^2¢/sin^2¢=cot^¢=(7/8)^2=49/64 |
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