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The value pi/12 is a solution for the equation: 4cos2 (4x) - 3 = 0. True or False.
Trigonometry is the study of the relationship of sides and angles of triangles. It has many applications in calculus and algebra.
Answer: False, x = π/12 is not a solution for the equation 4cos^{2} (4x) - 3 = 0.
Let's understand the solution in detail.
Explanation:
To check whether π/12 is a solution for the equation: 4 cos2 (4x) - 3 = 0, we put x = π/12 and check if the equation comes out to be zero.
Hence, we have y = 4 cos2 (4 (π/12)) - 3.
⇒ y = 4 cos2 (π/3) - 3
⇒ y = 4 × (1/2)2 - 3
⇒ y = 4 × 1/4 - 3
⇒ y = -2
Hence, x = π/12 is not a solution for the equation 4 cos2 (4x) - 3 = 0.
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