arctan(x)=arccos(3/4)

解答

arctan (x) = arccos (\frac{3}{4})

x = \frac{7}{3}

求解步骤

arctan (x) = arccos (\frac{3}{4})

使用反三角函数性质

arctan (x) = arccos (\frac{3}{4})

arctan (x) = a \Rightarrow x = tan (a)

x = tan (arccos (\frac{3}{4}))

tan (arccos (\frac{3}{4})) = \frac{7}{3}

tan (arccos (\frac{3}{4}))

使用三角恒等式改写:

tan (arccos (\frac{3}{4})) = \frac{1 - ( \frac{3}{4} ) ^{2}}{( \frac{3}{4} )}

利用以下特性:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{3}{4} ) ^{2}}{( \frac{3}{4} )}

= \frac{1 - ( \frac{3}{4} ) ^{2}}{\frac{3}{4}}

化简

= \frac{7}{3}

x = \frac{7}{3}

x = \frac{7}{3}

tan^{2} (θ) + 7 tan (θ) + 9 = 0

so l v e f or x, cos (x) \cdot cos (y) = 0

3 sec (θ) = 6

cot (x) = csc (x) + 3

cos (x) \cdot cos (3 5^{\circ}) = 1 - sin (x) \cdot sin (3 5^{\circ})