Find the value of \(\sin^2\theta + \cos^2\theta\).[Figure: right-angled Δ ABC, ∠ABC = 90º, ∠C = θ, with AB the side opposite θ and BC the side adjacent to θ.]Solution :In Δ ABC, ∠ABC = 90º, ∠C = θ.AB2 + BC2 = ____ ............ (Pythagoras theorem)Div…

Q.2 (A)(2) Find the value of \(\sin^2\theta + \cos^2\theta\).

[Figure: right-angled Δ ABC, ∠ABC = 90º, ∠C = θ, with AB the side opposite θ and BC the side adjacent to θ.]

Solution :

In Δ ABC, ∠ABC = 90º, ∠C = θ.

AB² + BC² = ____ ............ (Pythagoras theorem)

Divide both sides by AC²

\(\dfrac{AB^2}{AC^2} + \dfrac{BC^2}{AC^2} = \dfrac{AC^2}{AC^2}\)

∴ \(\left(\dfrac{AB}{AC}\right)^2 + \left(\dfrac{BC}{AC}\right)^2 = 1\)

But \(\dfrac{AB}{AC}\) = ____ and \(\dfrac{BC}{AC}\) = ____

∴ \(\sin^2\theta + \cos^2\theta\) = ____