If tan θ = 1 and sin θ = 1/√2, then the value of cos (θ + ϕ) is:

Question

If tan θ = 1 and sin θ = \(\frac1{\sqrt2}\), then the value of cos (θ + ϕ) is:

(a) –1 

(b) 0 

(c) 1 

(d) \(\frac{\sqrt3}{2}\)

Answer 1

(b) 0

tan θ = 1 ⇒ tan θ = tan 45° ⇒ θ = 45° 

sin ϕ = \(\frac1{\sqrt2}\)⇒ sin ϕ = sin 45° ⇒ ϕ = 45° 

∴ cos (θ + ϕ) = cos (45° + 45°) 

= cos 90° = 0