证明 cos(7a)+cos(a)=2cos(4a)cos(3a)

解答

证明

cos (7 a) + cos (a) = 2 cos (4 a) cos (3 a)

真

求解步骤

cos (7 a) + cos (a) = 2 cos (4 a) cos (3 a)

调整左侧

cos (7 a) + cos (a)

使用三角恒等式改写

cos (7 a) + cos (a)

使用和差化积恒等式:

cos (s) + cos (t) = 2 cos (\frac{s + t}{2}) cos (\frac{s - t}{2})

= 2 cos (\frac{7 a + a}{2}) cos (\frac{7 a - a}{2})

化简

2 cos (\frac{7 a + a}{2}) cos (\frac{7 a - a}{2}) : 2 cos (4 a) cos (3 a)

2 cos (\frac{7 a + a}{2}) cos (\frac{7 a - a}{2})

\frac{7 a + a}{2} = 4 a

\frac{7 a + a}{2}

p ro v e tan (x) sin (x) - sin (x) = 0

p ro v e tan (a) = \frac{( sin ( a ) )}{cos ( a )}

p ro v e cos (2 x) = sin (2 x)

p ro v e \frac{3 sin ^{2} ( 2 x )}{2} = \frac{3 cos ( 4 x )}{4}

p ro v e cos (θ) = 3