Question

if theta=sin^-1(x)+cos^-1(x)-tan^-1(x) and x>0 or x=0 then
optins-1)45<theta<90
2)0<theta<180

Answer 1

Answer on Question #67239 – Math – Trigonometry

Question

if theta=sin^(-1(x)+cos^(-1(x)-tan^(-1(x) and x>0 or x=0 then options

1) 45<theta<90 (2)="" 0<theta<180="" 2)="" angle="" on="" rule="" theta="">

Solution

Using complementary angles rule for $\cos^{-1}x = \frac{\pi}{2} - \sin^{-1}x$ we can obtain

$$\theta = \sin^{-1}x + \cos^{-1}x - \tan^{-1}x = \sin^{-1}x + \left(\frac{\pi}{2} - \sin^{-1}x\right) - \tan^{-1}x = \frac{\pi}{2} - \tan^{-1}x$$

Range of $\tan^{-1}x$ is $\left[-\frac{\pi}{2}; \frac{\pi}{2}\right]$

Range of $\theta = \frac{\pi}{2} - \tan^{-1}x$ is $[0; \pi]$

The range for $\theta$ will be $0{}^\circ < \theta < 180{}^\circ$.

Answer: 2) $0{}^\circ < \theta < 180{}^\circ$

Answer provided by https://www.AssignmentExpert.com</theta<90>