標題:
F.2 Maths x3
發問:
simplify the following expressions. 1. [1 / (cos^2 θ)] -1 2. 1 + tan^2 θ without using calculators, evalute the expressions. 1. sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o *please show the process, thanks.
最佳解答:
1. [1 / (cos^2 θ)] -1 =(1-cos^2 θ)/cos^2 θ =(sin^2 θ + cos^2 θ - cos^2 θ)/cos^2 θ =sin^2 θ/cos^2 θ =tan^2 θ 2. 1 + tan^2 θ =1+ (sin^2 θ / cos^2 θ) =(cos^2 θ + sin^2 θ) / cos^2 θ =1 / cos^2 θ without using calculators, evalute the expressions. 1. sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o We already know that, sin 45 o = (2^1/2)/2, cos 45 o = (2^1/2)/2, sin 30 o =1/2, cos 60 o =1/2, tan 60 o =1/(3^1/2) i.e., sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o =[(2^1/2)/2]^2 - [(2^1/2)/2]^2 + 1/2*1/2 + 1/(3^1/2) =1/4 + 1/(3^1/2) =1/4 + (3^1/2 /3) =[3 + 4 * (3^1/2)] / 12 2007-08-22 19:32:15 補充： Sorry..打錯左tan 60 o =3^1/2i.e.,sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o =[(2^1/2)/2]^2 - [(2^1/2)/2]^2 + 1/2*1/2 + 3^1/2=1/4 + 3^1/2
其他解答:
. simplify the following expressions 1. = cos^2 θ 2 1 + tan^2 θ = 1 + sin^2 θ over cos^2 θ =cos^2 θ over cos^2 θ + sin^2 θ over cos^2 θ = 1 over cos^2 θ without using calculators, evalute the expressions 1. sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o = 2.732050808 = 2.73 ( cor . in . hte nearest 0.01)
F.2 Maths x3
發問:
simplify the following expressions. 1. [1 / (cos^2 θ)] -1 2. 1 + tan^2 θ without using calculators, evalute the expressions. 1. sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o *please show the process, thanks.
最佳解答:
1. [1 / (cos^2 θ)] -1 =(1-cos^2 θ)/cos^2 θ =(sin^2 θ + cos^2 θ - cos^2 θ)/cos^2 θ =sin^2 θ/cos^2 θ =tan^2 θ 2. 1 + tan^2 θ =1+ (sin^2 θ / cos^2 θ) =(cos^2 θ + sin^2 θ) / cos^2 θ =1 / cos^2 θ without using calculators, evalute the expressions. 1. sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o We already know that, sin 45 o = (2^1/2)/2, cos 45 o = (2^1/2)/2, sin 30 o =1/2, cos 60 o =1/2, tan 60 o =1/(3^1/2) i.e., sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o =[(2^1/2)/2]^2 - [(2^1/2)/2]^2 + 1/2*1/2 + 1/(3^1/2) =1/4 + 1/(3^1/2) =1/4 + (3^1/2 /3) =[3 + 4 * (3^1/2)] / 12 2007-08-22 19:32:15 補充： Sorry..打錯左tan 60 o =3^1/2i.e.,sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o =[(2^1/2)/2]^2 - [(2^1/2)/2]^2 + 1/2*1/2 + 3^1/2=1/4 + 3^1/2
其他解答:
. simplify the following expressions 1. = cos^2 θ 2 1 + tan^2 θ = 1 + sin^2 θ over cos^2 θ =cos^2 θ over cos^2 θ + sin^2 θ over cos^2 θ = 1 over cos^2 θ without using calculators, evalute the expressions 1. sin^2 45 o - cos^2 45 o + sin 30 o * cos 60 o + tan 60 o = 2.732050808 = 2.73 ( cor . in . hte nearest 0.01)
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