Question

in in some buildings especially in industries the rules in client this inclination of rope application of trigonometric function .here the roof of industry is inclined at angles a and b. Determine the value of sin (a+b) if cosec a= root2 and cot b = 1 , where both a and b are acute angles.​

Answer 1

Hope it helps.. ..........

Answer 2

Sin(α + β) = 1

Step-by-step explanation:

Sin(α + β) = SinαCosβ  + CosαSinβ

cosecα = √2

=> 1/Sinα = √2

=> Sinα = 1/√2

Sin²α + Cos²α = 1

=>  (1/√2)² +  Cos²α = 1

=> 1/2 + Cos²α = 1

=> Cos²α =  1/2

=> Cosα =  1/√2

cot β = 1

=> Cosβ /Sinβ = 1

=> Cosβ  = Sinβ

Sin²β + Cos²β = 1

=> Sin²β + Sin²β = 1

=> 2Sin²β = 1

=> Sin²β = 1/2

=> Sinβ =  1/√2

& Cosβ = 1/√2

Sin(α + β) = SinαCosβ  + CosαSinβ

= (1/√2)(1/√2) + (1/√2)(1/√2)

= 1/2 + 1/2

= 1

Sin(α + β) = 1

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