Question 47

Find the value of $$tan 10^\circ tan 15^\circ tan 80^\circ tan 75^\circ$$

Solution

We have (tan10 tan15 tan80 tan75)

= Where tan(90-θ)=cotθ hence tan80=tan(90-10)=cot 10

Where cotθ is the inverse of tanθ

= In the same way tan75=tan(90-15)=cot 15

= Where cot 10=(1/tan10) & cot 15=(1/tan15)

=(tan10 × tan15 × $$\frac{1}{tan10}$$×$$\frac{1}{tan15}$$)

= 1

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