If + cosec = 2 , then ^2 + cose c ^ 2 = - Vidyadip

MCQ

If $\sin \theta + {\rm{cosec}}\theta = {\rm{2}}$, then ${\sin ^2}\theta + {\rm{cose}}{{\rm{c}}^{\rm{2}}}\theta = $

A
$1$
B
$4$
✓
$2$
D
None of these

✓

Answer

Correct option: C.

$2$

c
(c) ${\sin ^2}\theta + {\rm{cose}}{{\rm{c}}^2}\theta $

$= {(\sin \theta + {\rm{cosec}}\theta )^2} - 2\sin \theta {\rm{ cosec}}\theta $

$ = {(2)^2} - 2 = 4 - 2 = 2,$

since $(\sin \theta + {\rm{cosec}}\theta ) = 2.$

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