Prove that (Sin- cosec)2 +(cos- sec)2=(cot)2+(Tan)2-1.
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Step-by-step explanation:
LHS
=(sinA+cosecA)
2
+(cosA+secA)
2
=sin
2
A+cosec
2
A+2sinA.cosec A+cos
2
A+sec
2
A+2cosA.secA
=sin
2
A+cos
2
A+2+2+cosec
2
A+sec
2
A
=5+(1+cot
2
A)+(1+tan
2
A) ........ [sin²θ+cos²θ=1], [sec
2
θ=1+tan
2
θ] and [cosec
2
x=1+cot
2
x]
=7+tan
2
A+cot
2
A
= RHS
Hence, proved that
(sinA+cosec A)
2
+(cosA+secA)
2
=7+tan
2
A+cot
2
A
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