cscx = sinx tan x + cos x
Using xsx x = 1/sin x and tan x = sin x/cos x
[tex] \frac{1}{sin x} = sinx *\frac{sinx }{cos x} + cosx [/tex]
[tex] \frac{1}{sin x} = \frac{sin^2x +cos^2x}{cos x} [/tex]
[tex] \frac{1}{sin x} = \frac{1}{cos x} [/tex]
Multiplying both sides by cos x
[tex] \frac{cos x}{sin x} = 1 [/tex]
cot x =1
Correct option is d .
Answer: d. cotx=1
Step-by-step explanation: cosecx=sinxtanx+cosx
⇒ cosecx= sinx×[tex]\frac{sinx}{cosx}[/tex] +cosx
⇒ cosecx=[tex]\frac{sin^{2}x }{cosx}[/tex] +cosx
⇒ cosecx= [tex]\frac{sin^{2}x+cos^{2} x }{cosx}[/tex]
⇒ cosecx= 1/cosx (since sin²x+cos²x=1)
⇒ 1/sinx=1/cosx
⇒ cosx/sinx=1
⇒ cotx=1
