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

1.	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» (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

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»

(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