Question

prove that:
cos^2 A - sin A - 1/4 = 0​

Answer 1

Solution:

cos²A-sinA-1/4 = 0

multiply each term by 4 , we get

=> 4cos²A-4sinA-1 = 0

=> 4(1-sin²A)-4sinA-1=0

/* cos²A = 1-sin²A */

=> 4-4sin²A-4sinA-1=0

=> -4sin²A-4sinA+3=0

=> 4sin²A+4sinA -3 =0

Splitting the middle term, we get

=> 4sin²A+6sinA-2sinA-3 = 0

=> 2sinA(2sinA+3)-1(2sinA+3)=0

=> (2sinA+3)(2sinA-1)=0

=> 2sinA+3 =0 or 2sinA-1 = 0

=> sinA = -3/2 or sinA = 1/2

sinA -3/2 [ it is not possible ]

Therefore,

sinA = 1/2

=> sinA = sin30°

=> A = 30°

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