Question

Prove that: Sin^2+Cos^2=1
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Answer 1

Answer:

sin^2 A+cos^2A=1

This rule applies for every perpendicular base and hypotenuse

Let Perpendicular be P

Base be B

Hypotenuse be H

sin=P/H

cos=B/H

(P/H)^2+(B/H)^2=1

P^2/H^2+B^2/H^2=1

(P^2+B^2)/H^2=1

As we know according to Pythagoras theoram P^2+B^2=H^2

Substituting this to H^2 we get:

H^2/H^2=1 (H^2 cancelled out)

1=1

Since,LHS=RHS

Hence,proved

Answer 2

Step-by-step explanation:

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

By definition

sinθ=b/c(hypotenuseopposite side)

cosθ=a/c(hypotenuseadjacent side)

sin2θ+cos2θ=c2b2+c2a2=c2a2+b2

From Pythagoras theorem

c2=a2+b2

∴c2a2+b2=1

sin2θ+cos2θ=1