Question

Triangle abc is an isosceles right triangle,with ab as hypotenuse.find cos2b-1

Answer 1

see attachment,
here it is clear that AB is hypotenuse of triangle ABC.

we know, According to question,
triangle ABC is isosceles right angled triangle.
so, AC = BC and angle ACB = 90°

because AC = BC then, angle CAB = angle CBA = { Let x }

we also know, sum of all angles of any triangle equal to 180° .
so, angle ACB + angle CAB + angle CBA = 180°
90° + x + x = 180°
2x = 180° - 90°
x = 45°
hence, angle CAB = angle CBA = 45°

now, we have to find ( cos2B - 1 )
means we have to find ( cos2∠CBA - 1 )
but ∠CBA = 45°
so, cos2B - 1
= cos2(45°) -1 = cos90° -1 = 0-1 = -1