Question

In a right angle ABC, right angled at C, in which AB = 29 units, BC = 21 units and angleABC = ø , then the value of cos²ø-sin²ø=
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Answer 1

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By Pythagoras theorem,

AB 2

=AC 2

+BC 2

⇒AC2

=AB 2

−BC 2

⇒AC 2

=29

2 −21 2

=(29+21)(29−21)=50×8

⇒AC

2

=25×16

⇒AC=5×4=20 units

⇒cosθ=

ABBC

= 2921

,

sinθ= AB AC

= 2920

⇒sin2θ+cos 2

θ= 29 2 21 2 +20 2

= 29 2 29 2

=1

⇒cos

2 θ−sin 2 θ= 29 2

21 2 −20 2

= 841 41 .

Answer 2

Answer :

In ΔACB,

By Pythagoras theorem,

(AB)2=(AC)2+(BC)2

⇒(AC)2=(AB)2 −(BC)2

⇒(AC)2=(29)2−(21)2

⇒(AC)2= 841 - 441

⇒(AC)2= 400

⇒AC = ✓400

⇒ AC = 20

⇒(cos)2θ−(sin)2θ=(21)2−(20)2 = 41

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