Question

In an isosceles triangle ABC, AB = BC = 6 cm and ∠B = 90°. Find the values of cos² C + cosec² C

Answer 1

ΔABC is an isosceles right-angled triangle.
∴ AC²
= AB² + BC²
= 6² + 6²
= 36 + 36
= 72
⇒ AC = `6sqrt(2)"cm"`
cos² C + cosec² C

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

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

= `(5)/(2)`.