prove that (sec²A+cosec²A)½ = tan A+cotA
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Step-by-step explanation:
sec² x = 1+ tan² x
And
cosec² x =1+ cot²x
And
tan x.cot x = 1
━━━━━━━━━━━━━━━━━━━━━━━━━
Taking LHS.
√(1+ tan ²A) + (1+ cot² A) }
√( tan² A + cot² A+2)
√( tan²A +cot²A + 2 tan A.cot A)
━━━━━━━━━━━━━━━━━━━━━━━━━
√(tan A+ cot A)²
= tan A + cot A = RHS
━━━━━━━━━━━━━━━━━━━━━━━━━
Hence;
Proved √(sec² A + cosec² A) = tan A + cot A
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