Question

[tex]If 1+ sin ^{2} α = 3 sinα cosα, then \: values \: of \: cot α \: are
\ \textless \ br /\ \textgreater \ (a) -1, 1 (b) 0,1 (c)1, 2 (d) -1,-1[/tex]
${ \underline{ \boxed{\mathbb{\orange{note}}}}} \\ { \underline{ \boxed{\mathbb{\red{need \: quality answer}}}}} { \underline{ \boxed{\mathbb{\red{ with \: proper \: explation}}}}}$

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Answer 1

Answer:

option: (c) 1,2

Step-by-step explanation:

1+sin²a = 3sina.cosa

sin²a+cos²a+sin²a -3sina.cosa=0

2sin²a-3sina.cosa+cos²=0

2sin²a-2sina.cosa-sina.cosa+cos²a=0

2sina(sina-cosa)-cosa(sina-cosa)=0

(sina-cosa)(2sina-cosa)=0

so,

sina-cosa=0 , cosa=sina or, cota = 1.

2sina-cosa=0 , cosa=2sina or, cota = 2.

Note:

sin²a+cos²a = 1 and cosa/sina = cota.