Question

1) If Cos A=
2/3
2
5
then find the value of 4 + 4 tan? A.​

Answer 1

Answer:

The answer will be 25.

Explanation:

Given;

cos A = 2/5;

Asked : 4 + 4tan^2 A;

Solution:

So, cos A = 2/5;

sec A = 1/cos A

Thus, sec A = 5/2

Square both side;

sec^2 A = 25/4

Now, we know that, sec^2 θ = tan^2 θ + 1;

Thus, tan^2 A + 1 = 25/4;

Multiply 4 on both side;

Hence, 4(tan^2 A + 1) = (25/4) × 4;

4tan^2 A + 4 = 25;

Therefore, 4 + 4tan^2 A = 25.

That's all.

Answer 2

Given: CosA= 2/5

Side adjacent to angle A = 2

Hypotenuse. 5

AB = 2

AC. 5

Let AB = 2x & AC = 5x

Using Pythagoras Theorem to find AC

(Hyp)² = (Height)² + (Base)²

(5x)² = (2x)² + (BC)²

(BC)² = (5x)² - (2x)²

(BC)² = 25x² - 4x²

(BC)² = 21x²

BC = √21x

Now,

tanA = Side opposite to angle A

Side Adjacent to angle A

tanA = BC

AB

tanA = √21x

2x

tanA = √21

2

Thus,

4 + 4tan²A

= 4 + 4 (√21/2)²

= 4 + 4 × 21/4

= 4 + 21

= 25