Question

sin^2 theta or cos^2 theta me square kyu rahata hai kyu lagate hai theta me kyu nii rhata please koi batao.

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Answer 1

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.

Answer 2

Answer :- Sin^2(theta)+Cos^2(theta)=1 (Trigonomoetric Identity)

Therefore, sin^2(theta)=1-cos^2(theta)

Putting this value into given equation as per question,

we get, sin^2(theta)-cos^2(theta)=1-cos^2(theta)-cos^2(theta)

Thereby, sin^2(theta)-cos^2(theta)=1–2cos^2(theta)

Value of cos theta ranges from 0 to 1. So, in either case, the result can never be equal to 2.

The final result would be ,sin^2(theta)-cos^2(theta)=1–2cos^2(theta) and this is also a well known and widely used trigonometric identity.