9) Prove that (1+ tan ²theeta)(1+1/tan²theeta)=1/sin²theeta-sin⁴theeta
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Step-by-step explanation:
(1+tan²A)(1+1/tan²A)
=sec²A(tan²A+1/tan²A)
=sec²A(sec²A/tan²A)
=sec⁴A×cos²A/sin²A
=1/cos⁴A×cos²A/sin²A
=1/sin²Acos²A
=1/sin²A(1-sin²A)
=1/sin²A-sin⁴A
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