Evaluate the value of tan63-cot23-tan27-cot67-tan63- tan67-

Tan63^∘+cot23^∘/tan27^∘+cot67^∘ tan63^∘ tan67^∘ =cot27^∘+1/tan23^∘/1/cot27^∘+tan23^∘ tan63^∘ tan 67^∘ tan23^∘ cot27^∘+1 =tan23^∘/1+cot27^∘ tan23^∘/cot27^∘ ta ...

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Standard XII

Physics

Introduction

Evaluate the ...

Question

Evaluate the value of $\frac{t a n 63^{\circ} + c o t 23^{\circ}}{t a n 27^{\circ} + c o t 67^{\circ}} - t a n 63^{\circ} t a n 67^{\circ}$ .

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Solution

$\frac{t a n 63^{\circ} + c o t 23^{\circ}}{t a n 27^{\circ} + c o t 67^{\circ}} - t a n 63^{\circ} t a n 67^{\circ} = \frac{c o t 27^{\circ} + \frac{1}{t a n 23^{\circ}}}{\frac{1}{c o t 27^{\circ}} + t a n 23^{\circ}} - t a n 63^{\circ} t a n 67^{\circ} t a n 23^{\circ} c o t 27^{\circ} + 1 = \frac{t a n 23^{\circ}}{\frac{1 + c o t 27^{\circ} t a n 23^{\circ}}{c o t 27^{\circ}}} - t a n 63^{\circ} t a n 67^{\circ} = c o t 27^{\circ} c o t 23^{\circ} - c o t 27^{\circ} c o t 23^{\circ} = 0$

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Evaluate the value of tan63∘+cot23∘tan27∘+cot67∘−tan63∘tan67∘.

tan63∘+cot23∘tan27∘+cot67∘−tan63∘tan67∘=cot27∘+1tan23∘1cot27∘+tan23∘−tan63∘tan67∘tan23∘cot27∘+1=tan23∘1+cot27∘tan23∘cot27∘−tan63∘tan67∘=cot27∘cot23∘−cot27∘cot23∘=0

Evaluate the value of $\frac{t a n 63^{\circ} + c o t 23^{\circ}}{t a n 27^{\circ} + c o t 67^{\circ}} - t a n 63^{\circ} t a n 67^{\circ}$ .