Question

if tanA =2 then find the values of other trignometric ratio​

Answer 1

Step-by-step explanation:

tan(theta) = 2

this means that opposite divided by adjacent is equal to 2.

this can occur if opposite = 2 and adjacent = 1

this would make hypotenuse equal to sqrt(2^2 + 1^2) = sqrt(5).

your other functions would then be:  

sin (theta) = opp/hyp = 2/sqrt(5) = 2*sqrt(5)/5  

cos(theta) = adj/hyp = 1/sqrt(5) = sqrt(5)/5  

tan(theta) = opp/adj = 2/1 = 2  

cot(theta) = adj/opp = 1/2  

sec(theta) = hyp/adj = sqrt(5)/1 = sqrt(5)  

csc(theta) = hyp/opp = sqrt(5)/2

Answer 2

As per given,

$\tanA = 2$

And A lies in first quadrant

So

$\tan(A) = 2 = \frac{P}{B} \\ = > \frac{2}{1} = \frac{p}{b} \\ \: \: \: \: \: \: means \\ = > p = 2 \: \: \: and \: \: b = 1 \\ \: \: \: \: by \: using \: pythagoras \\ = > h = \sqrt{5}$

So

• $\sin(a) = \frac{p}{h} = \frac{2}{ \sqrt{5} }$
• $\cos(a) = \frac{b}{h} = \frac{1}{ \sqrt{5} }$
• $\tan(a) = 2$
• $\csc(a) = \frac{h}{p} = \frac{ \sqrt{5} }{2}$

Hope It Helps

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