Question

If \sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha&lt13;, then $\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)$ is equal to

• A. $16-5 \pi$
• B. 16
• C. 0
• D. $\pi$

Answer 1

Answer: (D)

$\pi$

Answer 2

cos−154​=tan−143​
∴sin−117α​=tan−13677​−tan−143​=tan−1(1+3677​⋅43​3677​−43​​)
sin−117α​=tan−1158​=sin−1178​
⇒17α​=178​⇒α=8
∴sin−1(sin8)+cos−1(cos8)
=3π−8+8−2π
=π