Please explain how to find sin a * cos a - cos b * sin b?

Question

Key word is EXPLAIN.

For example, please EXPLAIN how to find sin46 * cos1 - cos46 * sin1

Next, please explain how to find cos a * cos b - sin a * sin b
-- Example - please explain how to find cos 80 8 cos 10 - sin 80 * sin 10

Lastly please explain how to find (tan 200 - tan 20) / (1 + tan 200 * tan 20)

Answer 1

given your example, I assume your first question is how to find sina*cosb - cosa*sinb



you should know the following equation:



(1) sin(a+b) = sinacosb + cosasinb



so, in your first example, lets take a=46 and b=-1. we will have:



sin(46-1) = sin(45) = sqrt(2)/2 = sin(46)cos(-1) + cos(46)sin(-1) = sin(46)cos(1) - cos(46)sin(1)



Next, you should know that:



(2) cos(a+b) = cosa*cosb - sina*sinb



so your example:



cos 80 * cos 10 - sin 80 * sin 10 = cos(80+10) = cos(90) = 0



lastly, you can show that:



(3) tan(a+b) = (tana+tanb)/(1-tana*tanb)



using a = 200, b = -20, you get:



tan(200-20) = tan(180) = 0 = (tan 200 - tan 20) / (1 + tan 200 * tan 20)

Answer 2

it should be

sina cosb - cosa sinb = sin( a- b)

sin46 cos1 - cos46 sin1 = sin(46-1) = sin45 = 1/sqrt2 ans

cos80 cos10 - sin80 sin10= cos( 80+10) = cos90 =0

tan200- tan 20/(1+ tan200tan20

= tan( 200 - 20) = tan 180 = 0 [ tan(a-b) = tana- tanb/(1+tan tanb ]

Answer 3

sin(a + b) = sin a·cos b + cos a·sin b cos(a + b) = cos a·cos b - sin a·sin b .·. sin(a + b)·cos b - cos(a + b)·sin b = (sin a·cos b + cos a·sin b)·cos b - (cos a·cos b - sin a·sin b)·sin b = sin a·cos^2 b + cos a·cos b·sin b - cos a·cos b·sin b + sin a·sin^2 b center words cancel, leaving: sin a·cos^2 b + sin a·sin^2 b ingredient out sin a: sin a·(cos^2 b + sin^2 b) Use the identity cos^2 b + sin^2 b = a million: sin a· a million = sin a