Question

Diketahui sin A sin B = 2/9 dan tan A tan B = 1/3. nilai dari cos (a-b)/ cos (a+b) = ......

Answer 1

Tan a tan b = 1/3
sin a/cos a × sin b/cos b=1/3
sin a × sin b/cos a × cos b =1/3
2/9 / cos a× cos b=1/3
cos a × cos b = 2/9 × 3
cos a × cos b =2/3

shg,
cos (a-b)/ cos (a+b) = cos a cos b + sin a sin b/ cos a cos b- sin a sin b = 2/3+2/9 / 2/3-2/9 = 8/9 / 4/9= 8/4 = 2