RRB Junior Engineer Stage 1 Model Papers 9

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Question : 30 of 100

Marks: +1, -0

In a right-angled triangle ABC, ∠B is the right angle and AC

=2√5\cm

If

AB – BC = 2 cm

, then the value of

\cos^2 A-\cos^2 C

is:

$2/5$
$3/5$
$6/5$
$3/10$

Solution:

Let BC = x

∴ AB = x + 2

⇒(x+2)^2+x^2=(2√5)^2

⇒x^2+4x+4+x^2=20

⇒2x^2+4x-16=0

⇒x^2+2x-8=0

⇒x^2+4x-2x-8=0

⇒x(x+4)-2(x+4)=0

⇒(x-2)(x+4)=0

⇒x=2=BC

∴AB=2+2=4 \cm

\cos^2 A-\cos^2 C={AB^2}/{AC^2}-{BC^2}/{AC^2}

=16/20-4/20=12/20=3/5

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