Question

If tan a= 2 , then find the value of other trigonometric ratios.​

Answer 1

Let a be $\alpha$

Given :-

$tan \alpha = 2$

Solution :-

$tan \alpha = 2 \\ tan \alpha = \frac{2}{1} \\ tan \alpha = \frac{opp}{adj} = \frac{2}{1}$

By Using Pythagoras Theorem.,

$= \geqslant {(hyp)}^{2} = {(opp)}^{2} + {(adj)}^{2} \\ = \geqslant {(hyp)}^{2} = {(2)}^{2} + {(1)}^{2} \\ = \geqslant {(hyp)}^{2} = 4 + 1 \\ = \geqslant {(hyp)}^{2} = 5 \\ = \geqslant (hyp) = \sqrt{5}$

Hence,

opp = 2

adj = 1

hyp = √5

Now..

The ratios are...,

$\sin( \alpha) = \frac{opp}{hyp} = \frac{2}{ \sqrt{5} } \\ \cos( \alpha ) = \frac{adj}{hyp} = \frac{1}{ \sqrt{5} } \\ \tan( \alpha ) = \frac{opp}{adj} = \frac{2}{1} = 2 \\ \csc( \alpha ) = \frac{hyp}{opp} = \frac{ \sqrt{5} }{2} \\ \sec( \alpha ) = \frac{hyp}{adj} = \frac{ \sqrt{5} }{1} = \sqrt{5} \\ \cot( \alpha ) = \frac{adj}{opp} = \frac{1}{2}$

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