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Step-by-step explanation:
sin
2
A/cos
2
A+cos
2
A/sin
2
A
after applying lcm,
\begin{gathered}sin^4+cos^4/sin^2A.cos^2A\\=(sin^2A)^2+2sin^2A.cos^2A+(cos^2A)^2/sin^2A.cos^2A\end{gathered}
sin
4
+cos
4
/sin
2
A.cos
2
A
=(sin
2
A)
2
+2sin
2
A.cos
2
A+(cos
2
A)
2
/sin
2
A.cos
2
A
by using the identity a^2+b^2a
2
+b
2
=(a+b)^2-2ab=(a+b)
2
−2ab
\begin{gathered}(1)^2-2(sin^2A.cos^2A)/sin^2A.cos^2A\\=1/sin^2A.cos^2A-2(sin^2A.cos^2A)/sin^2A.cos^2A\\=1/sin^2A.cos^2A-2\\=1/1/sec^2A.cosec^2A-2\\=cosec^2A.sec^2A-2\end{gathered}
(1)
2
−2(sin
2
A.cos
2
A)/sin
2
A.cos
2
A
=1/sin
2
A.cos
2
A−2(sin
2
A.cos
2
A)/sin
2
A.cos
2
A
=1/sin
2
A.cos
2
A−2
=1/1/sec
2
A.cosec
2
A−2
=cosec
2
A.sec
2
A−2
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