Find the value of angle θ which satisfies both the equations tan θ = - 1 and cos θ = 1/√2

Question

Find the value of angle θ which satisfies both the equations tan θ = - 1 and cos θ = \(\frac{1}{\sqrt2}\)

Answer 1

We have

tan θ = - 1

tan θ = tan 135°

tan θ = tan (180° + 135°)

tan θ = tan 135° or tan 315°

θ = 135° or 315° ......... (i)

Again for equation cos θ = \(\frac{1}{\sqrt2}\)

cos θ = cos 45° or cos(360° - 45°)

cos θ = 45° or cos θ = 315°

θ = 45° or 315° ............ (ii)

Taking common value in equation (j) and (ii)

θ = 315° = \(\frac{7\pi}{4}\)

Thus, general value of θ = 2nπ + \(\frac{7\pi}{4}\), n ∈ Z