Math, asked by singhaditibhardwaj, 5 months ago

prove that (sec²A+cosec²A)½ = tan A+cotA​

Answers

Answered by thebrainlykapil
103

Step-by-step explanation:

\huge\color{red}{ We \:know \:that:}

sec² x = 1+ tan² x

And

cosec² x =1+ cot²x

And

tan x.cot x = 1

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\huge\color{green}{ Solution:}

Taking LHS.

\sf\blue{  √(sec²A\: + \:cosec² A)}

√(1+ tan ²A) + (1+ cot² A) }

√( tan² A + cot² A+2)

√( tan²A +cot²A + 2 tan A.cot A)

━━━━━━━━━━━━━━━━━━━━━━━━━

\huge\color{green}{ Using:}

\sf\blue{  (a² \:+\:b²\: +\: 2ab)  \:= \:(a \:+\: b)²}

√(tan A+ cot A)²

= tan A + cot A = RHS

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Hence;

Proved √(sec² A + cosec² A) = tan A + cot A

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