Question

If 3 tan A=4, then find sin A and cos A.​

Answer 1

Step-by-step explanation:

$3 \tan\alpha = 4 \\ = > \tan\alpha = \frac{4}{3} \\ \\ we \: know \: { \sec\alpha }^{2} - { \tan\alpha }^{2} = 1 \\ \\ { \sec\alpha }^{2} - { (\frac{4}{3}) }^{2} = 1 \\ = > { \sec\alpha }^{2} = 1 + \frac{16}{9} \\ = > { \sec\alpha }^{2} = \frac{25}{9 } \\ = > { \sec \alpha }^{} = \frac{5}{3} \\ = > \cos \alpha = \frac{3}{5} \\ \\ we \: also \: know \: { \sin\alpha }^{2} + { \cos \alpha }^{2} = 1 \\ \\ { \sin \alpha }^{2} = 1 - \frac{9}{25} \\ = > { \sin\alpha }^{2} = \frac{16}{25} \\ = > \sin\alpha = \frac{4}{5}$

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Answer 2

Question

If 3 tan A = 4, Then Find sin A and cos A

$\rule{350}{1}$

3 tan A = 4

⇒ (3 tan A)/3 = 4/3

⇒ tan A = 3/4

⇒ Opposite / Adjacent = 3/4

Comparing This We get

• Opposite = 3 & Adjacent = 4

We also need to get Hypotenuse to find sin A and cos A

(Hypotenuse)² = (Opposite)² + (Adjacent)²   .....(By Pythagoras Theorem)

⇒ (Hypotenuse)² = 3² + 4²

⇒ (Hypotenuse)² = 9 + 16

⇒ (Hypotenuse)² = 25

⇒ Hypotenuse = √25

⇒ Hypotenuse = 5

$\rule{350}{1}$

sin A = Opposite / Hypotenuse

⇒ sin A = 3/5

cos A = Adjacent / Hypotenuse

⇒ cos A = 4/5