Question

the value of [tan30°•sin60°•cosec30°/sec0°•cot60°•cos30°]4 is equal to

Answer 1

$\frac{ \tan(30) \times \sin(60) \times \cosec(30) }{ \sec(0) \times \cot(60) \cos(30) } \times 4 \\ = \frac{ \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{2} \times 2}{1 \times \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{2} } \times 4$

$= \frac{1}{ \frac{1}{2} } \times 4 \\ = 2 \times 4 \\ = 8$

Answer 2

Solution:

The value of the given expression is 16

Explanation:

We have to find the value of the expression

$\left [\frac{ \tan 30^{\circ} \cdot \sin 60^{\circ} \cdot \csc 30^{\circ}}{\sec 0^{\circ}\cdot \cot 60^{\circ}\cdot \cos 30^{\circ}  }   \right ] ^4$

We can evaluate the value of the expression by using the standard value of the given trigonometric function.

$\left [\frac{( 1/\sqrt3) \cdot (\sqrt3 /2)\cdot 2}{1\cdot (1/\sqrt3)\cdot (\sqrt3 /2 ) }   \right ] ^4$

On simplifying the numerator and denominator, we get

$\frac{1}{1/2}\\\\=(2)^4\\\\=16$