ans this multiple choice question in maths with solution
If sina+sinB =p, cosa+cos B=q, then which of the following is always true? 2 (a) p² + q² ≥ 4 (c) p² +q² ≥5 (b) p² + q² ≤4 (d) p² +q² ≥7
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Answer:
sinA
=p;
cosB
cosA
=q
sinA=psinB−−−(1);cosA=qcosB−−−(2)
tanA=
q
p
tanB−−−(3)(dividing(1)by(2))sinAcosA=pqsinBcosB(Multiply(1)&(2))
cos
2
Acos
2
B
sinAcosA
=
cos
2
Acos
2
B
pqsinBcosB
=sec
2
BtanA=pqsec
2
AtanB
=(1+tan
2
B)tanA=pq(1+tan
2
A)tanB
=[1+(
q
p
tanA)
2
]tanA=pq(1+tan
2
A).
q
p
tanA(by(3))
=1+
q
2
p
2
tan
2
A=q
2
+q
2
tan
2
A
=tan
2
A(
p
2
q
2
−q
2
)=q
2
−1
=tan
2
A
q
2
−p
2
q
2
(q
2
−1)p
2
tanA=
q
2
(p
2
−1)
p
2
(1−q
2
)
=
q
p
p
2
−1
1−q
2
tanB=
p
2
−1
1−q
2
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