If 2sinβ – cosβ = 2 , then β is - Maths

If 2`"sin"^{2}`β – `"cos"^{2}`β = 2 , then β is

(a) 0ᵒ

(b) 90ᵒ

(c) 45ᵒ

(d) 30ᵒ

(b) 90ᵒ 

Explanation:

= 2`"sin"^{2}`β – `"cos"^{2}`β = 2

= `"-cos"^{2}`β = 2 - 2`"sin"^{2}`β

= `"-cos"^{2}`β = 2 (1 - `"sin"^{2}`β)

= `"-cos"^{2}`β = 2 `"cos"^{2}`β 

= `"-cos"^{2}`β - 2 `"cos"^{2}`β = 0

= 3`"cos"^{2}`β = 0

 = `"cos"^{2}`β = 0

   = cosβ = 0

This is Possible if β = `90^{2}`

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CBSE Class 10 Mathematics Sample Paper-2022