Question

If x sin (90° − θ) cot (90° − θ) = cos (90° − θ), then x =
(a) 0
(b) 1
(c) −1
(d) 2

Answer 1

SOLUTION :  

The correct option is  (b) : 1

Given : x sin (90° -θ ) cot (90° -θ ) = cos (90° -θ )

x sin (90° -θ ) cot (90° -θ ) = cos (90° -θ)

x cos θ tan θ = sin θ

[cos (90 - θ) = sin θ , sin (90° -θ ) = cos θ, cot (90° -θ ) = tan θ]

x cos θ × (sin θ/cos θ) = sin θ

[tan θ = sin θ/cos θ]

x sin θ = sin θ

x = sin θ/sin θ

x = 1

Hence, the value of x is 1 .

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

Option(B)

Step-by-step explanation:

Given Equation is x sin(90 - θ) cot(90 - θ) = cos(90 - θ)

∴ sin(90 - θ) = cosθ, cot(90 - θ) = tanθ, cos(90 - θ) = sinθ

⇒ x cosθ * tanθ = sinθ

⇒ x tan θ = (sinθ/cosθ)

⇒ x tanθ = tanθ

⇒ x = 1

Therefore, value of x = 1.

Hope it helps!