Question

K sin a=√3, K cos a=1 where K>0 and 0<a<90°. The values of K and a are​

Answer 1

Answer:

given, k sin a = √3 and k cos a = 1

to find, a and k

now, k sin a/k cos a= √3/1

> sin a /cos a= √3

> tan a = √3

> tan a = tan 60°

therefore a = 60° answer

now, k cos a = 1

k cos 60° = 1

k *1/2 = 1

therefore, k = 2 answer

Answer 2

Answer:

k = 2 and a = 60°

Step-by-step explanation:

Given :

• ksin a = √3         ⇒ sin a  = √3 / k
• kcos a = 1            ⇒ cos a = 1 / k

We know that

sin² a + cos² a = 1

Substituting the values of sin a and cos a

⇒ ( √3 / k )² + ( 1 / k )² = 1

⇒ ( √3 )² / k² + 1² / k²= 1

⇒ 3 / k² + 1 / k² = 1

⇒ ( 3 + 1 ) / k² = 1

⇒ 4 / k² = 1

⇒ 4 = k²

Taking square root on both sides

⇒ √4 = k

⇒  2 = k

⇒ k = 2

Substituting k in sin a = √3 / k and cos a = 1 / k

• sin a = √3 / 2     ⇒ a = 60°
• cos a = 1 / 2       ⇒ a = 60°

Hence the value of k is 2 and a is 60°.