If sin x = \(\frac{5}{13}\) and 0o \(\leq\) x \(\leq\) 90o, find the value of (cos x - tan x)

If sin x = \(\frac{5}{13}\) and 0^o \(\leq\) x \(\leq\) 90^o, find the value of (cos x - tan x)

Answer Details

We know that sin x = \(\frac{5}{13}\) and 0^o \(\leq\) x \(\leq\) 90^o. First, we can find the value of cos x using the identity: sin² x + cos² x = 1 sin² x + cos² x = 1 \(\frac{25}{169}\) + cos² x = 1 cos² x = \(\frac{144}{169}\) cos x = \(\pm\)\(\frac{12}{13}\) Since 0^o \(\leq\) x \(\leq\) 90^o, we know that cos x is positive. Therefore, cos x = \(\frac{12}{13}\). Next, we can find the value of tan x using the identity: tan x = \(\frac{sin x}{cos x}\) tan x = \(\frac{sin x}{cos x}\) = \(\frac{\frac{5}{13}}{\frac{12}{13}}\) = \(\frac{5}{12}\) Finally, we can find the value of (cos x - tan x) as: cos x - tan x = \(\frac{12}{13}\) - \(\frac{5}{12}\) = \(\frac{79}{156}\) Therefore, the answer is (cos x - tan x) = \(\frac{79}{156}\).