Question

• To
To verify the trigonometric identity sin^2theta+cos^2theta=1 experimentally using graph
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Answer 1

Answer:

ANSWER

Let a, b, c be lengths of right angled triangle

By definition

sinθ=b/c(

hypotenuse

opposite side

)

cosθ=a/c(

hypotenuse

adjacent side

)

sin

2

θ+cos

2

θ=

c

2

b

2

+

c

2

a

2

=

c

2

a

2

+b

2

From Pythagoras theorem

c

2

=a

2

+b

2

∴

c

2

a

2

+b

2

=1

sin

2

θ+cos

2

θ=1

Hence, proved.

Step-by-step explanation:

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Answer 2

Answer:

Let ABC be the right angled triangle at B

By using Pythagoras theorem, we get

Base ^2 + Perpendicular^2 = Hypotenuse^2

AB^2 + BC^2 = AC ^2

Now dividing both sides by AC^2 , we get

AB^2/AC^2 +BC^2/AC^2 = AC^2/AC^2

cos^2 theta + sin^2 theta = 1 (base/hypotenuse=cos theta and perpendicular/hypotenuse=sin theta)

or, sin^2 theta + cos^2 theta = 1

HENCE PROVED