If m = sin A, n = cos A, then show that : Tan A +Cot A/Tan A - Cot A = n Sin A + m Cos A /n Sin A - m Cos A = n2 + m2/n2 - m2
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they are not the same thing that I have to be a good time to
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If m=cosA−sinA and n=cosA+sinA; show that
m
2
−n
2
m
2
+n
2
=−
2
1
secA.cosecA=−
2
(cotA+tanA)
.
Answer
m=cosA-sinA , m=cosA+sinA.
m
2
−n
2
m
2
+n
2
=
(cosA−sinA)
2
−(cosA+sinA)
2
(cosA−sinA)
2
(cosA+sinA)
2
=
(cosA−sinA+cosA+sinA)(cosA−sinA−cosA−sinA)
cos
2
A+sin
2
A−2cosAsinA+cos
2
A+sin
2
A+2cosAsinA
=
2cosA(−2sina)
1+1
=
−4cosAsinA
2
=
2
−1
secAcosA.
=
2cosAsinA
−1
=
2sin2A
−1
[∵sin2θ=2sinθcosθ]
=
1+tan
2
A
2tan4
−1
[∵sin2θ=
1+tan
2
θ
2tan
2
θ
]
=
2tanA
−(1+tan
2
A)
=
2
−1
(
tana
1
+
tanA
tan
2
A
)
=
2
−1
(cotA+tanA)
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