Question

3. If 3cos 2 A + 7sin 2 A = 4 , show that cotA = √3​

Answer 1

Answer:

cot A = cot 30° = √3

Step-by-step explanation:

Given,

7 sin²A + 3 cos²A = 4

or,3 sin²A + 3 cos²A + 4 sin²A = 4

or, 3 ( sin²A + cos²A ) + 4 sin²A = 4

Now, sin²A + cos²A = 1 from basic identity.

or, 3 + 4 sin²A = 4

or, sin²A = 1/4

or, sin A = 1/2

1/2 can be written as sin 30°:

or, sin A = sin 30°

or, A = 30°

Since, A = 30°, we can find value of cotA.

or, cot A = cot 30° = √3

Hence Proved!