Question

Solve : [Trigonometry]

Sec²x + cosec²x
$\geqslant$
4

fast...

Answer 1

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⏩sec² + cosec² = (1+tan²x)+1(cot²x)

⏩2 + tan²x + cot²x

⏩2 + tan²x +cot²x -2tanx•cotx +2tanxcotx


putting tanx•cotx = 1

⏩2+(tanx - cotx)² +2

⏩4+(tanx -cotx)² >= 4

⏩by using identity

(tanx -cotx)² >= 0

Reason is the tanx and cot x are complementary phased chande of Π


Thank.

Answer 2

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