Question

PROVE THAT. square root of (sec^2 A + cosec^2 A )= sec A . cosec A​

Answer 1

Step-by-step explanation:

Question:-

PROVE THAT. square root of (sec^2 A + cosec^2 A )= sec A . cosec A.

Answer:-

√(sec2A + cosec2A) = tanA + cotA

$LHS = √(sec2A + cosec2A)$

$= \sqrt{ \frac{1}{cos {}^{2} A} + \frac{1}{sin {}^{2}A } }$

$= \sqrt{ \frac{sin {}^{2}A + cos {}^{2} A}{sin {}^{2} A \: cos {}^{2} A} }$

$= \: \sqrt{ \frac{1}{sin {}^{2}A \: cos {}^{2}A } }$

$= \: \sqrt{ \frac{1}{sin \: A \: cos \: A} }$

$RHS = tan \: A \: + cot \: A$

$= \: \frac{sinA}{cosA} \: + \: \frac{cosA}{sinA}$

$= \: \frac{sin {}^{2}A \: + \: cos {}^{2} A }{sin \: A \: cos \: A}$

$= \: \frac{1}{sin \:A \: cos \: A}$

Hence, LHS = RHS ( Proved)

Answer 2

Answer:

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