Question

prove that : √sec2 A + cosec2 A = tan A + cotA​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

we know, from trigonometric identities

$sec^2x-tan^2x=1$

then, $sec^2A-tan^2A=1$

$\implies sec^2A=1+tan^2A$....(1)

similarly, $cosec^2x-cot^2x=1$

then,$cosec^2A-cot^2A=1$

$\implies cosec^2A=1+cot^2$.....(2)

LHS = $\sqrt{sec^2A+cosec^2}$

putting equations (1) and (2),

= $\sqrt{1+tan^2A+1+cot^2A}$

= $\sqrt{tan^2A+cot^2A+2tanA.cotA}$

[ as we know, tanA . cotA = 1 so, we can write 2 = 2tanA.cotA ]

= $\sqrt{(tanA+cotA)^2}$

= tanA + cotA = RHS