Question

Find a numerical value of one trigonometric function of x for cscx=sinxtanx+cosx

a.sinx=0
b.cotx=0
c.sinx=1
d.cotx=1

Please Explain How This is Done.

Thanks!

Answer 1

Answer: d. cotx=1

Step-by-step explanation: cosecx=sinxtanx+cosx

⇒ cosecx= sinx×
`(sinx)/(cosx)` +cosx

⇒ cosecx=
`(sin^(2)x  )/(cosx)` +cosx

⇒ cosecx=
`(sin^(2)x+cos^(2) x )/(cosx)`

⇒ cosecx= 1/cosx (since sin²x+cos²x=1)

⇒ 1/sinx=1/cosx

⇒ cosx/sinx=1

⇒ cotx=1

Answer 2

cscx = sinx tan x + cos x

Using xsx x = 1/sin x and tan x = sin x/cos x

`(1)/(sin x) = sinx *(sinx )/(cos x) + cosx`

`(1)/(sin x) = (sin^2x +cos^2x)/(cos x)`

`(1)/(sin x) = (1)/(cos x)`

Multiplying both sides by cos x

`(cos x)/(sin x) = 1`

cot x =1

Correct option is d .