Question

For 0° ≤theta ≤ 90°, draw an appropriate figure and prove that: Sin²theta+cos²theta=1​

Answer 1

Answer:

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

Hence, proved.