The value of (tan30ᵒcosec60ᵒ+ tan60ᵒsec30ᵒ)/(sin²30ᵒ + 4cot²45ᵒ - sec²60ᵒ) is:

The value of (tan30ᵒcosec60ᵒ+ tan60ᵒsec30ᵒ)/(sin²30ᵒ +…

The value of (tan30^ocosec60^o+ tan60^osec30^o)/(sin²30^o + 4cot²45^o - sec²60^o) is:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e 32/3.

Understanding/Application

= (tan30⁰ cosec60⁰ + tan60⁰sec30⁰)/(sin²30⁰ + 4cot²45⁰ - sec²60⁰)

Putting the values -

= (1/ ${\sqrt{3} }$ × 2/ ${\sqrt{3} }$ + ${\sqrt{3} }$ × 2/ ${\sqrt{3} }$ )/(1/2² + 4 × 1 - 2²)

= (2/3 + 2)/(1/4 + 4 - 4)

= (8/3)/(1/4)

= 32/3