Question

if tanA=1/3,then find the value of cos2A and sin2A​

Answer 1

Answer:

cos2A = 4/5 and sin2A = 3/5

Step-by-step explanation:

we know that

cos2A = 1-tan²A/1+tan²A

=> 1- (1/3)²/1+(1/3)²

=> 1-1/9 / 1+1/9

=> 8/9 / 10/9

=> 4/5

and also ,

sin2A = 2tan²A/1+tan²A

=> 2×(1/3) / 1+ (1/3)²

=> (2/3) / 1 +(1/9)

=> 2/3 / 10/9

=> 3/5

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Answer 2

Given :

• tanA=1/3

To find :

• Cos2A
• Sin2A

Solution :

We know that :-

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

Therefore , the value of Sin2A :-

${ \rm \implies sin \: 2A = \dfrac{2tanA}{1 + {tan}^{2}A } }$

It is given that :- tanA=1/3

${ \rm \implies sin \: 2A = \dfrac{2 \times \frac{1}{3} }{1 + {( \frac{1}{3}) }^{2}} }$

${ \rm \implies sin \: 2A = \dfrac{ \frac{2}{3} }{1 + {( \frac{1}{9}) }} }$

${ \rm \implies sin \: 2A = \dfrac{ \dfrac{2}{3} }{{ \dfrac{9 + 1}{9} }} }$

${ \rm \implies sin \: 2A = \dfrac{ \frac{2}{3} }{{ \frac{10}{9} }} }$

${ \rm \implies sin \: 2A = \dfrac{2}{3} } \times {{ \dfrac{9}{10} }}$

${ \rm \implies sin \: 2A = \dfrac{1}{1} } \times {{ \dfrac{3}{5} }}$

$\rm \implies sin \: 2A = \dfrac{3}{5}$

Therefore , value of Sin 2A = 3/5

Now we will find out the value of Cos2A.

We know that :-

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

${ \rm \implies cos \: 2A = \dfrac{1 - {tan}^{2}A}{1 + {tan}^{2}A } }$

It is given that :- tanA=1/3

tan²A =( 1/3)² = 1/9

${ \rm \implies cos \: 2A = \dfrac{1 - \frac{1}{9} }{1 + \frac{1}{9} } }$

${ \rm \implies cos \: 2A = \dfrac{ \frac{9 - 1}{9} }{ \frac{9 + 1}{9} } }$

$\rm \implies cos \: 2A = \dfrac{8}{10} = \dfrac{4}{5}$

Therefore , value of Cos 2A = 4/5

Answer :

• Sin 2A = 3/5
• Cos 2A = 4/5