Question

if sin A=1/✓5 sin B =1/✓10 find the values of cos A and cos B .using the formula cos(A+B)=cosA.cosB-sinA.sinB, show that A+B=45

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Given ::- sin A = 1/√5

SinB = 1/√10

Solution ::-

Sin²A + Cos²A = 1

Cos²A = 1 - sin²A

= 1 - (1/√5)²

= 1 - 1/5

Cos²A = 4/5

Cos A = 2/√5 .........taking sq. rt. on both sides

Sin²B + cos²B = 1

Cos²B = 1 - sin²B

= 1 - (1/√10)²

= 1 - 1/10

Cos²B = 9/10

CosB = 3/√10 .........taking sq. rt on both sides

Using given equation ::-

Cos(A+B) = cosA.cosB-sinA.sinB

Cos(2/√5 + 3/√10) = 2/√5 x 3/√10 - 1/√5 x 1/√10

LHS ::-

2/√5 x 3/√10 - 1/√5 x 1/√10

= 6/√50 - 1/√50

= 5/√50

= 5/√50 x √50/√50 ........rationalising

= 5√50 / 50

= √50/ 10

= 5√2 / 10 ........∵√50 = 5√2

= √2/2

= √2/2 x √2/√2 .......multiplying by √2/√2

= 2/2√2

= 1/√2

But , cos 45° = 1/√2

From RHS,

Cos(A+ B) = 1/√2

So, cos(A+ B) = cos45°

Therefore,

A + B = 45°

HENCE PROVED

HOPE IT HELPS YOU!!