Question

If 1+ sin a 3 sina cosa, then values of cot a are
(a)-1, 1
(b) 0,1
(c)1,2
(d)-1,-1​

Answer 1

Answer:

(c) 1,2 is the correct answer

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf 1 + { \sin}^{2} A = 3 \sin A \cos A$

TO DETERMINE

The value of cot A are

(a) - 1 , 1

(b) 0 , 1

(c) 1 , 2

(d) - 1 , - 1

EVALUATION

Here it is given that

$\displaystyle \sf 1 + { \sin}^{2} A = 3 \sin A \cos A$

We solve it as below

$\displaystyle \sf 1 + { \sin}^{2} A = 3 \sin A \cos A$

$\displaystyle \sf \implies { \sin}^{2} A + { \cos}^{2} A+ { \sin}^{2} A = 3 \sin A \cos A$

$\displaystyle \sf \implies { \cos}^{2} A+ 2{ \sin}^{2} A - 3 \sin A \cos A = 0$

Dividing both sides by sin²A we get

$\displaystyle \sf \implies { \cot}^{2} A+ 2 - 3 \cot A = 0$

$\displaystyle \sf \implies { \cot}^{2} A - 3 \cot A + 2 = 0$

$\displaystyle \sf \implies { \cot}^{2} A - 2 \cot A - \cot A+ 2 = 0$

$\displaystyle \sf \implies \cot A (\cot A - 2) -( \cot A - 2) = 0$

$\displaystyle \sf \implies (\cot A - 2) ( \cot A - 1) = 0$

$\displaystyle \sf \implies \cot A = 2 \:, \: 1$

FINAL ANSWER

Hence the correct option is (c) 1 , 2

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