The value of sin-1 ( cos ( 53 π/5)) is

Question

The value of sin-1 ( cos ( 53 π/5)) is (A)  (3 π/5) (B)  (-3 π/5) (C)  (π/10) (D)  (- π/10)

Tardigrade Admin · Accepted Answer

We have, sin -1( cos (53 π/5))= sin -1[ cos (10 π+(3 π/5))] = sin -1[ cos ((3 π/5))] [∵ cos (2 n π ± θ)= cos θ] = sin -1[ sin ((π/2)-(3 π/5))] = sin -1[ sin ((5 π-6 π/10))] = sin -1[ sin ((-π/10))]=(-π/10)

Q. The value of $sin^{- 1} (cos \frac{53 π}{5})$ is

$\frac{3 π}{5}$

$\frac{- 3 π}{5}$

$\frac{π}{10}$

$\frac{- π}{10}$

Q. The value of sin−1(cos553π​) is

53π​

5−3π​

10π​

10−π​

We have, sin−1(cos553π​)=sin−1[cos(10π+53π​)] =sin−1[cos(53π​)] [∵cos(2nπ±θ)=cosθ] =sin−1[sin(2π​−53π​)] =sin−1[sin(105π−6π​)] =sin−1[sin(10−π​)]=10−π​

Q. The value of $sin^{- 1} (cos \frac{53 π}{5})$ is

$\frac{3 π}{5}$

$\frac{- 3 π}{5}$

$\frac{π}{10}$

$\frac{- π}{10}$