Question

If 3 sin A = 4 cos A, then

Answer 1

Answer: 1/4

Step-by-step explanation:

Please see the attached file,

Answer 2

Step-by-step explanation:

Given :-

3 sin A = 4 Cos A

To find :-

Find the value of Sec^2 A/4(1+Tan^2 A) ?

Solution:-

Method-1:-

Given that

3 sin A = 4 Cos A

=> 3 Sin A / Cos A = 4

=> 3 Tan A = 4

=> Tan A = 4/3

On squaring both sides then

=> Tan^2 A = (4/3)^2

=> Tan^2 A = 16/9

On adding 1 both sides then

=> 1+ Tan^2 A = 1+(16/9)

=> 1+ Tan^2 A = (9+16)/9

=> 1+Tan^2 A = 25/9

We know that

Sec^2 A - Tan^2 A = 1

=> Sec^2 A = 1+Tan^2 A

Therefore, Sec^2 A = 25/9

Now , the value of Sec^2 A/4(1+Tan^2 A)

=> (25/9)/(4)(25/9)

=> 1/4

Method -2:-

Given that :-

3 sin A = 4 Cos A

The value of Sec^2 A/4(1+Tan^2 A)

We know that

Sec^2 A - Tan^2 A = 1

=> Sec^2 A = 1+Tan^2 A

now ,

Sec^2 A/4(1+Tan^2 A)

=> Sce^2 A/4(Sec^2 A)

=> 1/4

Answer:-

The value of Sec^2 A/4(1+Tan^2 A) is 1/4

Used formulae:-

• Sec^2 A - Tan^2 A = 1

• Tan A = SinA/ CosA