Question

7) Find the acute angle o such that 2cos²0=
3 sin0​

Answer 1

Answer:

2cos²∅ = 3 sin∅

=> 2( 1 - sin²∅ ) = 3sin∅

=> 2 - 2sin²∅ = 3sin∅

=> 2sin²∅ + 3sin∅ - 2 = 0

=> 2sin²∅ + 4sin∅ - sin∅ - 2 = 0

=> 2sin∅( sin∅ + 2) - 1 ( sin∅ + 2) = 0

=> ( sin∅ + 2)( 2sin ∅ - 1 ) = 0

=> sin∅ + 2 = 0 , or , 2sin∅ -1 = 0

=> sin∅ = -2 , or , sin∅ = ½

but the minimum value of sin∅ is ( -1 )

so, sin∅ = -2 is rejected..

thus,

sin∅ = ½

or , sin∅ = sin30°

OR, ∅ = 30° .

I hope it will help u .

Step-by-step explanation:

formula used ,

cos²∅ = 1 - sin²∅.

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