Question

if 1-cosA=1/2,show that tan^2 A +4sin^2 A=6

Answer 1

Answer:

Step-by-step explanation:

1 - CosA = 1/2

=> CosA = 1 - 1/2 = 1/2

=> CosA = Cos60°  (∵ Cos60° = 1/2)

=> A = 60°.

Now Tan²A +4 Sin²A

= Tan²60 + 4Sin²60

= (√3)² + 4 * (√3/2)²

= 3 + 4 * 3/4

= 3 + 3

= 6

= R.H.S  

Hence proved.

Answer 2

given

1 - cosA = 1/2

cosA =1 - 1/2

cosA = 1/2

A = 60°

Now

tan²A + 4sin²A

=tan²60° + 4sin²60°

=(√3)² + 4(√3/2)²

=3 + 4(3/4)

=3 + 3

=6