If sin 0 = 4/5
4/5 and cos e = = -3/5 then
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Step-by-step explanation:
Answer
In quadrant IV, cosθ>0,sinθ<0,cosϕ>0 and sinϕ<0.
Now, cos θ=
5
4
⇒sin
2
θ=(1−cos
2
θ)=(1−
25
16
=
25
9
⇒sinθ=−
25
9
=
5
−3
.And, cos ϕ=
13
12
⇒sin
2
ϕ=(1−cos
2
ϕ)=(1−
169
144
=
169
25
⇒sinϕ=−
169
25
=
13
−5
.
∴ cos(θ+ϕ)=cosθcosϕ−sinθsinϕ=(
5
4
×
13
12
)−(
5
−3
×
13
−5
)=(
65
48
−
65
15
)=
65
33
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