Question

if x=sin inverse sin(10),y=cos inverse cos (10) then find y-x

Answer 1

we know, $sin^{-1}(sinA)=A$ when -90° < A< 90°
and $cos^{-1}(cosA)=A$ when 0 < A < 180°

here, x = $sin^{-1}(sin10^{\circ})=10^{\circ}$ as it clear that, -90° < 10° < 90°

and y = $cos^{-1}(cos10^{\circ})=10^{\circ}$ as it is clear that, 0° < 10° < 180°

so, y - x = 10° - 10° = 0°

hence , y - x = 0°

Answer 2

HELLO DEAR,

as we know, sin-¹(sinx) = x [if , -90 < x < 90]
and cos-¹ (cosx) = x [if 0 < x < 180]

now,
given, x = sin-¹{sin(10)} & y = cos-¹{cos(10)}

so, x = 10 [if 0 < x < 90]

similarly,

y = cos-¹ (cos10) = 10 [if 0 < x < 180]

therefore, y - x = 10 - 10 = 0

I HOPE IT'S HELP YOU DEAR,
THANKS