If 3sec θ + 4 cos θ - 4 √(3) = 0 where θ is an acute angle then the value of θ is:

If 3sec θ + 4 cos θ - 4 √(3) = 0 where θ is an acute angle…

If 3sec $\theta$ + 4 cos $\theta$ - 4 $\sqrt{3}$ = 0 where $\theta$ is an acute angle then the value of $\theta$ is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 30º

Instead of solving this equation we could just use the substitution method and make our life easy,

⇒ $\theta$ = 45^o

⇒ 3 sec 45^o + 4 cos 45^o = 4√3

⇒ 3√2 + 4√2 = 5√2

This is not the correct answer.

⇒ $\theta$ = 60^o

⇒ 3 sec 60^o + 4 cos 60^o = 4√3

⇒ 3(2) + 4(1/2)

This is not the correct answer.

⇒ $\theta$ = 30^o

⇒ 3 sec 30^o + 4 cos 30^o = 4√3

⇒ 3(2/√3) + 4(√3/2)

⇒ 2√3 + 2√3 = 4√3

This is the correct answer.