cot4 θ + cot2 θ is equal to :
2 cot2 θ. cosec2 θ
tan2 θ + tan4 θ
tan2 θ.cosec2 θ
cosec4 θ - cosec2 θ
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Solving,
⇒ cot4 θ + cot2 θ
⇒ cot2 θ(cot2 θ + 1)
⇒ cot2 θ.cosec2 θ
Substituting, cot2 θ = cosec2 θ - 1, we get :
⇒ (cosec2 θ - 1).cosec2 θ
⇒ cosec4 θ - cosec2 θ.
Hence, Option 4 is the correct option.
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sin4 θ - cos4 θ is equal to :
sin2 θ - 1
1 + cos2 θ
2 sin2 θ - 1
1 - cos2 θ
(1 + tan θ)2 + (1 - tan θ)2 is equal to :
2 cosec2 θ
2 sec2 θ
cosec2 θ
sec2 θ