Question

if cos A = 3/root 10 , cos B = 2/root 3, A and B are positive acute angles , then the value of (A+B) is ?​

Answer 1

Step-by-step explanation:

sinA=

10

1

⇒A=sin

−1

(

10

1

)

sinB=

5

1

⇒B=sin

−1

(

5

1

)

Now,

A+B=sin

−1

(

10

1

)+sin

−1

(

5

1

)

As we know that,

sin

−1

A+sin

−1

B=sin

−1

(A

1−B

2

+B

1−A

2

)

∴A+B=sin

−1

(

10

1

1−

5

1

+

5

1

1−

10

1

)

A+B=sin

−1

(

50

2

+

50

3

)

⇒A+B=sin

−1

(

50

5

)

⇒A+B=sin

−1

(

2

1

)

⇒A+B=

4

π

(∵A and B are positive acute angles)

Hence the correct answer is

4

π

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Answer 2

Use principle/ general solution

to find Sin A and sin B