If cos P= 1/7 and cos Q =13/14 where P and Q both are acute angles,then value of P-Q is.......
Answers
Answered by
0
Answer:
We are given cosP=
7
1
& cosQ=
14
13
So, we know thta sin
2
θ+cos
2
θ=1
∴ cosθ=
1−sin
2
θ
or
sinθ=
1−cos
2
θ
−−−(1)
∴ sinP=
1−(
7
1
)
2
=
1−
49
1
=
48
/7
∴ sinQ=
1−(
14
13
)
2
=
1−
196
169
=
27
/14
let cos(P−Q)
=cosPcosQ+sinPsinQ
=
7
1
×
14
13
+
7
48
×
14
27
=
98
13
+
98
4
3
×3
3
=
98
13+36
=
98
49
=
2
1
∴ P−Q=cos
−1
(
2
1
)=
3
π
(as 0<P,Q<
2
π
)
∴ P−Q=(
3
π
) or (60
o
)
Similar questions