prove that tan²A+cot²A+2=sec²A×cosec²A
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Answer:
I hope you will like my answer and i hope you will understand it.* is used for multiplication while ^2 is used for square.
Explanation:
L.H.S.=tan^2A+cot^2A+2
=sin^2A/cos^2A+cos^2A/sin^2A+2
=(sin^4A+cos^4A+2sin^2Acos^2A)/ sin^2Acos^2A
=(sin^2A+cos^2A)^2/sin^2Acos^2A
=1/sin^2Acos^2A
=1/sin^2A*1/cos^2A
=cosec^2A*sec^2A
=sec^2A*cosec^2A
=R.H.S.
Hence Proved
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