Question

If cos tita=1/2 and tita is acute, then 4sin²tita+tan²tita =?​

Answer 1

Answer:

Step-by-step explanation:

Given that,

cos θ = 1/2 = BC / AC ( ∵ In the right angle triangle ABC, ∠B = 90° )

By using Pythagoras theorem, we have

AC² = AB² + BC²

( 2 )² = AB² + ( 1 )²

4 = AB² + 1

4 - 1 = AB²

AB² = 3

AB = √3

sin θ = AB / AC = √3 / 2

tan θ = AB / BC = √3 / 1 = √3

∴ 4 sin²θ + tan² θ = 4 (√3/2 )² + (√3)²

= 4 ( 3/4 ) + 3

= 3 + 3

= 6 is the answer.