If 270°

Question

If 270° < θ < 360° , then √2 + √2 + 2 cos θ is equal to (A) -2sin((θ /4)) (B) 2sin((θ /4)) (C) 2cos((θ /4)) (D) -2cos((θ /4))

Tardigrade Admin · Accepted Answer

√2 + √2 + 2 cos θ =√2 + √2 ⋅ 2 cos2 (θ /2) =√2 + 2 |cos (θ /2)|,135° < (θ /2) < 180° =√2 - 2 cos (θ /2)=|2 sin (θ /4)| , 67(1 ° /2) < (θ /4) < 90° =2sin(θ /4)

Q. If $27 0^{\circ} < θ < 36 0^{\circ}$ , then $2 + 2 + 2 cos θ$ is equal to

$- 2 s in (\frac{θ}{4})$

$2 s in (\frac{θ}{4})$

$2 cos (\frac{θ}{4})$

$- 2 cos (\frac{θ}{4})$

$2 + 2 + 2 cos θ = 2 + 2 \cdot 2 co s^{2} \frac{θ}{2}$
$= 2 + 2 ∣ ∣ cos \frac{θ}{2} ∣ ∣, 13 5^{\circ} < \frac{θ}{2} < 18 0^{\circ}$
$= 2 - 2 cos \frac{θ}{2} = ∣ ∣ 2 s in \frac{θ}{4} ∣ ∣$ ,
$67 \frac{1 ^{\circ}}{2} < \frac{θ}{4} < 9 0^{\circ} = 2 s in \frac{θ}{4}$

Q. If 270∘<θ<360∘ , then 2+2+2cosθ​​ is equal to

−2sin(4θ​)

2sin(4θ​)

2cos(4θ​)

−2cos(4θ​)