Latest self Aptitude Question SOLUTION: In a rt angled triangle ABC, ang B is the right angle and AC = 2rt5 cm. If AB-BC = 2cm, then the value of (cos^2A-cos^2C) is :

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In a rt angled triangle ABC, ang B is the right angle and AC = 2rt5 cm. If AB-BC = 2cm, then the value of (cos^2A-cos^2C) is :

Arjun (11 years ago)

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divya  (11 years ago)

ac=2rt5 ab=4 bc=2 (using a^2+b^2=C^2)
we get cos(A)=(4/2rt5)
and cos(c)=2/2rt5
cos^2A-cos^2c=3/5=.6

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karpagam  (11 years ago)

can u explain for me again

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divya  (11 years ago)

ac=2rt5 consider on of the other two sides be bc=x and third side will ab= 2+x(ab-bc=2)
so x^2+ (2+x)^2=(2rt5)^2
sloving this we get x=2
now cos(A)=ab/ac=4/2rt5
cos(C)=bc/ac=2/2rt5
then cos^2(a)-cos^2(c)=(4/2rt5)^2-(2/2rt5)^2
4/5-1/5=3/5=0.6

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snehil  (11 years ago)

AB-BC=2....(1)
sqar it
(AB-BC)^2=AB^2+BC^2-2AB.BC
but AB62+BC^2=(2sqt5)^2.... according to Pythagoras Thermo
put the vale u will get
AB.BC=8
now solve with eq(1)
AB=4
BC=2
now you have AB=4 BC=2 CA=2sqt5
and triangle is right angle
so find out cosA ,cosC and solve
ans will be 3/5

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