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If α  + β  = 90°, α = 2β, find the value of Cos2α  + Sin2β.  
1. 2/3
2. 1
3. 1/2
4. 4/3

1 Answer

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Correct Answer - Option 3 : 1/2

Given:

α  + β  = 90°

α = 2β 

Formula used:

Sin(90° - θ) = Cosθ 

Tan(90° - θ) = Cotθ 

Sec(90° - θ) = Cosecθ 

SinA + CosB = 1

then, A + B = 90°

Calculation:

α  + β  = 90°      ----(1)

α = 2β      ----(2) 

From the equation (1) and (2)

2β + β = 90°

⇒ 3β = 90°

⇒ β = 30°

Now, from (1) 

α = 2 × 30°

⇒ α = 60°

Now, we have to find the value of Cos2α  + Sin2β

Cos2 60° + Sin30°

⇒ 1/4 + 1/4

⇒ 1/2

∴ The value of cos260° + sin230° is 1/2.

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