Question

From the following figure, find the values of :
(i) sin A
(ii) sec A
(iii) cos² A + sin²A

Answer 1

Given angle, ABC = 90° in the figure

⇒ AC² = AB² + BC²       ...(AC is hypotenuse in Δ ABC )
⇒ AC² = a² + a²
∴ AC² = 2a² and AC =`sqrt2a`

Now

(i) sin A = `"perpendicular"/"hypotenuse" = "BC"/"AC" = a/(sqrt2a) = 1/(sqrt2)`

(ii) sec A = `"hypotenuse"/"base" = "AC"/"AB" = (sqrt2a)/a = sqrt2`

(iii) sin A = `"perpendicular"/"hypotenuse" = "BC"/"AC" = a/(sqrt2a) = 1/(sqrt2)`

cos A = `"base"/"hypotenuse" = "AB"/"AC" = a/(sqrt2a) = 1/(sqrt2)`

cos²A + sin²A  = `(1/(sqrt2))^2 + (1 /(sqrt2))^2`

= `(1)/(2) +(1)/ (2)`

= 1