If cosh x=(√14/3), sinh x= cos θ and -π

Question

If cosh x=(√14/3), sinh x= cos θ and -π<θ<-(π/2), then sin θ= (A) (1/3) (B) (2/3) (C) -(1/3) (D) -(2/3)

Tardigrade Admin · Accepted Answer

∵ cos h2 x- sin h2 x=1 ⇒ cos h2 x- cos 2 θ=1 [∵ sin h x= cos θ] ⇒ cos 2 θ= cos h 2 x-1 =(14/9)-1=(5/9) So, sin 2 θ=1- cos 2 θ=1-(5/9)=(4/9) ∵ -π<θ<-(π/2) ∴ sin θ=-(2/3)

Q. If $cosh x = \frac{14}{3}, sinh x = cos θ$ and
$- π < θ < - \frac{π}{2}$ , then $sin θ =$

$\frac{1}{3}$

$\frac{2}{3}$

$- \frac{1}{3}$

$- \frac{2}{3}$

Q. If coshx=314​​,sinhx=cosθ and −π<θ<−2π​, then sinθ=

31​

32​

−31​

−32​

∵cosh2x−sinh2x=1 ⇒cosh2x−cos2θ=1[∵sinhx=cosθ] ⇒cos2θ=cosh2x−1 =914​−1=95​ So, sin2θ=1−cos2θ=1−95​=94​ ∵−π<θ<−2π​ ∴sinθ=−32​

Q. If $cosh x = \frac{14}{3}, sinh x = cos θ$ and
$- π < θ < - \frac{π}{2}$ , then $sin θ =$

$\frac{1}{3}$

$\frac{2}{3}$

$- \frac{1}{3}$

$- \frac{2}{3}$