Question

if Sina=4/5,find sin3a​

Answer 1

Answer:

The Right Answer is:- 44/125

Step-by-step explanation:

Step 1:- Given that,

Sina=4/5 & then find Sin3a

Step 2:- We Know that,

Sin3a= 3Sina-4Sin^3a

Step 3:- Sin3a= 3*4/5-4*(4/5)^3

Step 4:- Sin3a= 12/5-4*(64/125)

Step 5:- Sin3a= 12/5-256/125

Step 6:- Sin3a= 300-256/125

Step 7:- Sin3a= 44/125

Answer 2

Given :

• Sin a = 4/5

To find :

• Sin3a

Solution :

We know that :-

$\rm \boxed { \large \rm sin \: 3 \theta =3 \: sin \theta - 4 {sin}^{3} \theta}$

Therefore, now :-

$\rm \implies { \large \rm sin \: 3 a =3 \: sin \: a - 4 {sin}^{3} a}$

It is given that :- Sin a = 4/5

sin³ a = (4/5)³ = 64/125

$\rm \implies { \large \rm sin \: 3 a =(3 \times \dfrac{4}{5} ) -( 4 \times \dfrac{64}{125} ) }$

$\rm \implies { \large \rm sin \: 3 a =\dfrac{12}{5} - \dfrac{256}{125}}$

LCM of 5 and 125 = 125

$\rm \implies { \large \rm sin \: 3 a = \dfrac{300 - 256}{125}}$

$\rm \implies { \large \rm sin \: 3 a = \dfrac{44}{125}}$

Answer :

• Sin 3a = 44/125

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Learn More :-

$\rm \boxed { \rm sin \: 2 \theta = \frac{2tan\theta}{1 + {tan}^{2} \theta}}$

$\rm \boxed { \rm Cos \: 2 \theta = \frac{1 - {tan}^{2} \theta}{1 + {tan}^{2} \theta}}$