Question

If CosA = 2/5 find the value of tan A + cot A

Answer 1

Heya mate, Here is ur answer

Cos A =2/5

Cos^2 A= (2/5)^2

=4/25

We know that

Sin^2 A= 1-cos^2 A

sin^2 A=1-4/25

Sin^2 A=25-4/25

Sin^2 A= 21 /25

Sin A=√21/√25

Sin A =√21/5

Now Tan A = Sin A/cos A

Cot A= Cos A+Sin A

So, Tan A+Cot A

$= \frac{sin \: a}{cos \: a} + \frac{cos \: a}{sin \: a}$


$= \frac{sin {}^{2}a + cos {}^{2} a }{sin \: a \: \times cos \: a}$


$= \frac{1}{ \frac{ \sqrt{21} }{5} \times \frac{5}{ \sqrt{21} } }$


$= \frac{1}{1}$


$= 1$


Warm regards

@Laughterqueen

Be Brainly ✌✌✌

Answer 2

tan A=sinA/CosA
value of Cot A=cosA/SinA
then
value of tanA+cotA
sinA/cosA+cosA/sinA
then
tanA=BC/AB
BUT COSA=AB/AC
AB=2
AB=5
BC=Square root 21
then tanA+cotA=
$\sqrt{21}$
then answer is 25/2×square root21