Question

sin
${sin}^{2} thata + {cos}^{2} thata = 1$
i want this explanation and answer
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Answer 1

Answer:

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

By definition

sinθ=b/c =(Opposite side/Hypotenuse)

cosθ=a/c(Adjacent side/Hypotenuse)

sin2  θ+cos2 θ= b2/c2+ a2+c2 = a2+b2/c2

From Pythagoras theorem

c2 =a2  +b2

a2+b2/c2 = 1

sin2  θ+cos2  θ=1

Hence, proved.

Answer 2

Answer:

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

Let a, b, c be lengths of right angled triangle.By definition,

sin^θ = b/c ( hypotenuse opposite side )

cos^θ = 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.

$thanks$