if tan²A=1+2tan²B prove that cos2B=1+2cos2A
dratul353:
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o yes
cos2B=1+2cos2A=1+2×(1-tan²A/1+tan²B)=1+(2{1-[1+2tan²B]}/{1+[1+2tan²B]}=1+(-4tan²B)/(2+2tan²B)=1+(-4tan²B)/(2+2tan²B)=(2+2tan²B-4tan²B)/(2+2tan²B)=(2-2tan²B)/(2+2tan²B)=2(1-tan²B)/2(1+tan²B)=cos2B
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