Question

If sin θ = cos θ, (0° < θ < 90°), then value of (sec θ · sin θ) is ______.

पर्याय

• `1/sqrt2`

• `sqrt2`

• 1

• 0

Answer 1

If sin θ = cos θ, (0° < θ < 90°), then value of (sec θ · sin θ) is 1.

Explanation:

Given

sin θ = cos θ 

⇒ `sin θ/cos θ = 1`

⇒ tan θ = 1

θ = `pi/4`

then (sec θ · sin θ)

Put θ = `pi/4            ...[(∴ sec  (pi)/(4) = sqrt2),(sin  (pi)/(4) = 1/sqrt2)]`

⇒ `sec  (pi)/(4) · sin  (pi)/(4)`

⇒ `sqrt2 · 1/sqrt2` 

= 1