Q11 Logic says answer is 0 degree because theta= 90 degree But how to show in paper or - Maths - Introduction to Trigonometry

Question

Q11 Logic says answer is 0 degree because theta= 90 degree But how
to show in paper or prove mathmeatically?

11   I f   s i n   θ 1   +   sin
  θ 2   +   sin   θ 3   =  
3 ,   0   <   θ 1 ,   θ 2 ,  
θ 3   ≤   90 °   F i n d   t h e
  v a l u e   o f   cos   θ 1   +
  cos   θ 2   +   cos   θ 3

Sanjari Kalantri · Accepted Answer

Dear Student,

Since 0 < θ1, θ2 and θ3 ≤ 90°,The minimum value of sinθ1, sinθ2 and sinθ3 is 0 and maximum value is 1
Given that sinθ1 + sinθ2 + sinθ3 = 3,This is only possible if sinθ1 = sinθ2 = sinθ3 = 1, or θ1 = θ2 = θ3 = 90°So, cosθ1 + cosθ2 + cosθ3= cos90° + cos90° + cos90°= 0 + 0 + 0= 0

Q11. Logic says answer is 0 degree because theta= 90 degree. But how to show in paper or prove mathmeatically? 11 . I f s i n θ 1 + sin θ 2 + sin θ 3 = 3 , 0 < θ 1 , θ 2 , θ 3 ≤ 90 ° . F i n d t h e v a l u e o f cos θ 1 + cos θ 2 + cos θ 3 .

Q11. Logic says answer is 0 degree because theta= 90 degree. But how to show in paper or prove mathmeatically?

$11 . I f s i n θ_{1} + \sin θ_{2} + \sin θ_{3} = 3, 0 < θ_{1}, θ_{2}, θ_{3} \leq 90 ° . F i n d t h e v a l u e o f \cos θ_{1} + \cos θ_{2} + \cos θ_{3} .$