Prove that (tanA + cotA)² + (sinA + cosecA)² + (cosA + secA)²=9 +2tan²A + cot²A
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cosec θ−cotθ)
2
=
1+cosθ
1−cosθ
(ii)
1+sinA
cosA
+
cosA
1+sinA
=2secA
(iii)
1−cotθ
tanθ
+
1−tanθ
cotθ
=1+secθcosec θ[Hint: Write the expression in terms of sinθ and cosθ
(iv)
secA
1+secA
=
1−cosA
sin
2
A
[Hint: Simplify LHS and RHS separately].
(v)
cosA+sinA+1
cosA−sinA−1
=cosec A+cotA, Using the identity cosec
2
A=1+cot
2
A
(vi)
1−sinA
1+sinA
=secA+tanA
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