Question

A) Given that sin x =cos x , find the value of tan x .

b) Find the values of x in the interval 0≤x<360 for which sin x =cos x .

Answer 1

`(a)\\\\\text{Given that, sin x = cos x }\\\\\text{So,} ~ \tan x = (\sin x)/(\cos x) = (\sin x)/(\sin x) = 1\\\\\\(b)\\\\\text{Given that,}\\\\\sin x = \cos x\\\\\implies (\sin x)/(\cos x) =1\\\\\implies \tan x =1\\\\\implies x = n\pi + \frac{\pi} 4 \\\\\text{For interval}~ [0, 2\pi),}\\\\x= \frac{\pi}4, \frac{5\pi}4~~;[\text{When n = 0,1}]\\\\\text{In degrees,} ~ x= 45^(\circ) , 225^(\circ)`