3 sin θ = 4cos θ find the value of 4sin^2 θ - 3 cos^2 θ +2
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Answer:
3sin² x + 4cos² x = 3sin² x + (3cos² x + cos² x)
= 3sin² x + 3cos² x + cos² x
= (3sin² x + 3cos² x) + cos² x
= 3(cos² x + sin² x) + cos² x
Since we have the trigonometric identity: cos² x + sin² x = 1, substituting, we get:
= 3(1) + cos² x
Therefore, we have the result:
= 3 + cos² x
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