Verify cos(a+b)/cos(a) cos(b) =1-tan(a) tan(b)

One  Way:

Cos( a+b ) / cos(a) cos(b)

(cosacosb - sina sinb) / cosa cosb (as from formula of cos(a + b ) = cosacosb - sinasinb

we can spilt the above line as,

cosacosb /cosacosb - sinasinb / cosacosb ( dividing cosacosb by cosacosb we got 1)

= 1 - ( sina/cosa- sinb/cosb)( you know sina/cosa = tana ,   and sinb/cosb = tanb )

= 1 - tan(a) tan(b) = RHS ( right hand side)

Another Way:

(cos(a+b)/ cos(a)cos(b))= 1 -tan(a)tan(b)

”Sum of Cosine Identity”

cos(A + B) = cos A cos B − sin A sin B

(cos(a)cos(b) - sin (a) sin(b))/cos(a)cos(b)=...

(cos(a)cos(b))/(cos(a)cos(b)) - (sin(a)sin(b))/(cos(a)cos(b))=

sin(x)/cos(x) = tan(x) such that...

(cos(a)cos(b))/(cos(a)cos(b)) = 1

(sin(a)sin(b))/(cos(a)cos(b)) = tan(a)tan(b)

1 - tan(a)tan(b) = 1 - tan(a)tan(b)

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b