1 Answer

WoutervD · Answer 1 · 2022-03-22T23:33:41+0000

Answer:

$\sin^2 A + cosec^2A = 7$

Step-by-step explanation:

Given

$\sin A+cosec\ A=3$

Required

Find
$\sin^2A + cosec^2A$

$\sin A+cosec\ A=3$

Square both sides

$(\sin A+cosec\ A)^2=3^2$

$(\sin A+cosec\ A)(\sin A+cosec\ A)=9$

Open brackets

$\sin^2 A + 2\sin A\ cosec\ A + cosec^2A = 9$

In trigonometry:

$cosec\ A = (1)/(\sin A)$

So, we have:

$\sin^2 A + 2\sin A *(1)/(\sin A) + cosec^2A = 9$

$\sin^2 A + (2\sin A)/(\sin A) + cosec^2A = 9$

$\sin^2 A + 2 + cosec^2A = 9$

Collect like terms

$\sin^2 A + cosec^2A = 9-2$

$\sin^2 A + cosec^2A = 7$

Please log in or register to add a comment.