sec^4X + sec^2X = tan^4X + tan^2X prove the statement
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Answer:
» L.H.S. = sec⁴x + sec²x
= 1/cos⁴x + 1/cos²x
= (1 + cos²x)/cos⁴x
= sin²x / cos⁴x
» R.H.S. = tan⁴x + tan²x
= sin⁴x/cos⁴x + sin²x/cos²x
= (sin⁴x + sin²x cos²x) / cos⁴x
= sin²x (sin²x + cos²x) / cos⁴x
= sin²x/cos⁴x
Since, L.H.S. = R.H.S.
Hence, proved.
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