Question

If 3cos² A + 7sin² A = 4, show that cotA= √3
please reply within 3:00pm​

Answer 1

Step-by-step explanation:

Given:-

3cos² A + 7sin² A = 4

To Show:-

cotA= √3

Using formula:-

Sin² A+ Cos ² A=1

=>Cos² A=1- Sin² A

=>Sin² A=1- Cos² A

Sin30°=1/2

Cot 30°=√3

Solution:-

Given that 3 cos² A+7 sin² A=4

we know that sin²A+cos² A=1

=>3(1-sin² A)+7sin²A=4

=>3-3 Sin² A+7 Sin² A=4

=>3+4 sin² A=4

=>4 Sin² A=4-3

=>4 Sin² A=1

=>Sin² A=1/4

=>Sin A=√(1/4)

=>Sin A=1/2

=>Sin A= Sin 30°

=>A=30°

Now ,

LHS:

Cot A

=>Cot 30°

=>√3

=RHS

LHS=RHS

Answer:-

CotA=√3

Hence,proved.