Question : Is the value of sinθ+cosθ is always greater than 1? Justify your answer.
Doubt by Jaskirta
Solution :
⭐ When θ = 0° then
sinθ+cosθ
=sin0°+cos0°
=0+1
=1
⭐ When θ = 30° then
sinθ+cosθ
=sin30°+cos30°
=1/2+√3/2
=(1+√3)/2
=(1+1.732)/2
= 2.732/2
= 1.366
⭐ When θ = 45° then
sinθ+cosθ
=sin45°+cos45°
= 1/√2 + 1/√2
= 2/√2
= √2
= 1.414
⭐ When θ = 60° then
sinθ+cosθ
=sin60°+cos60°
= √3/2 + 1/2
= (√3+1)/2
= (1.732+1)/2
= 2.732/2
= 1.366
⭐ When θ = 90° then
sinθ+cosθ
=sin90°+cos90°
= 1+0
= 1
Clearly at 0° and 90°, the value of sinθ+cosθ is less than 1.
Hence, we can say that the value of sinθ+cosθ is not always greater than 1.