Question

4 tan 60° sec 30° +
sin 31° sec 59° + cot 59° cot 31°
8 sin
2 30° − tan
2 45°

Answer 1

Answer:

The Value of given expression is 7.

Step-by-step explanation:

Given Expression is

$4\cdot tan60^{\circ}\cdot sec30^{\circ}+sin31^{\circ}\cdot sec59^{\circ}+cot59^{\circ}\cdot cot31^{\circ}-8\cdot sin^230^{\circ}-tan^245^{\circ}\\\\\implies4\cdot \sqrt{3}\cdot \frac{2}{\sqrt{3}}+sin31^{\circ}\cdot \frac{1}{cos59^{\circ}}+\frac{cos59^{\circ}}{sin59^{\circ}}\cdot \frac{cos31^{\circ}}{sin31^{\circ}}-8\cdot (\frac{1}{2})^2-(1)^2\\\\(Since,\:value\:of \:tan60^{\circ} = \sqrt{3},\:sec30^{\circ}=\frac{2}{\sqrt{3}},\:sin30^{\circ}=\frac{1}{2}\:and\:tan45^{\circ}=1)\\\\\implies8+\frac{sin31^{\circ}}{sin(90-59)^{\circ}}+\frac{cos59^{\circ}}{cos(90-59)^{\circ}}\times\frac{cos31^{\circ}}{cos(90-31)^{\circ}}-\frac{8}{4}-1\\\\(Since,\:sin\,\theta=cos(90-\theta)\:and\: cos\,\theta=sin(90-\theta))\\\\\implies8+\frac{sin31^{\circ}}{sin31^{\circ}}+\frac{cos59^{\circ}}{cos31^{\circ}}\times\frac{cos31^{\circ}}{cos59^{\circ}}-2-1\\\\\implies8+1+1-2-1\\\implies7$

Therefore, The Value of given expression is 7.