If sin(sin-1 (1/5)+cos-1x) = 1, then the value of x is

Question

If sin(sin-1 (1/5)+cos-1x) = 1, then the value of x is (A) -1 (B) (2/5) (C) (1/3) (D) (1/5)

Tardigrade Admin · Accepted Answer

We have, sin(sin-1 (1/5)+cos-1x) = 1 ⇒ sin-1 (1/5)+cos-1x = sin-1(1) ⇒ sin-1 (1/5)+ (π/2) -sin-1 x = (π /2) ⇒ sin-1 (1/5) -sin-1 x = 0 ⇒ sin-1 (1/5) = sin-1 x ⇒ x = sin (sin-1 (1/5)) ⇒ x = (1/5)

Q. If $s in (s i n^{- 1} \frac{1}{5} + co s^{- 1} x) = 1$ , then the value of $x$ is

$- 1$

$\frac{2}{5}$

$\frac{1}{3}$

$\frac{1}{5}$

Q. If sin(sin−151​+cos−1x)=1, then the value of x is

−1

52​

31​

51​

We have, sin(sin−151​+cos−1x)=1 ⇒sin−151​+cos−1x=sin−1(1) ⇒sin−151​+2π​−sin−1x=2π​ ⇒sin−151​−sin−1x=0 ⇒sin−151​=sin−1x ⇒x=sin(sin−151​) ⇒x=51​

Q. If $s in (s i n^{- 1} \frac{1}{5} + co s^{- 1} x) = 1$ , then the value of $x$ is

$- 1$

$\frac{2}{5}$

$\frac{1}{3}$

$\frac{1}{5}$