If sec A tan B+ tan A sec B=2, sec A sec B+ tan A tan B =k, k²=
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MATHS
If secAtanB+tanAsecB=91, then the value of (secAsecB+tanAtanB)
2
is equal to
December 20, 2019
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Vrinda Nimbalkar
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ANSWER
Given secAtanB+tanAsecB=91
Squaring both sides, we get
⇒sec
2
Atan
2
B+tan
2
Asec
2
B+2tanAtanBsecAsecB=8281
⇒2tanAtanBsecAsecB=8281−sec
2
Atan
2
B−tan
2
Asec
2
B ...(1)
Consider, (secAsecB+tanAtanB)
2
=sec
2
Asec
2
B+tan
2
Atan
2
B+2tanAtanBsecAsecB
=sec
2
Asec
2
B+tan
2
Atan
2
B+8281−sec
2
Atan
2
B−tan
2
Asec
2
B (by (1))
=sec
2
A−tan
2
A+8281
=8282
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