The-most-general-value-of-which-satisfy-both-the-equations-cos-1-2-and-tan-1-is-

Question Number 43642 by gunawan last updated on 13/Sep/18

The most general value of θ which

satisfy both the equations \cos θ = - \frac{1}{\sqrt{2}}

and \tan θ = 1 is

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Sep/18

c o s θ = - v e t a n θ = + v e s o θ l i e s i n t h i r d q u a d r a n t

t a n θ = 1 = t a n (Π + \frac{Π}{4}) θ = \frac{5 Π}{4}

c h e c k \dots

c o s (Π + \frac{Π}{4}) = - c o s (\frac{Π}{4}) = - \frac{1}{\sqrt{2}}

t a n θ = t a n \frac{5 Π}{4}

θ = x Π + \frac{5 Π}{4} x = 2 θ = \frac{13 Π}{4}

c o s θ = c o s (\frac{5 Π}{4})

θ = 2 y Π \pm \frac{5 Π}{4}

θ = 2 y Π + \frac{5 Π}{4} y = 1 θ = \frac{13 Π}{4}