Question 63

Find the value of tan 4° tan 43° tan 47 tan 86°

Solution

Expression : tan 4° tan 43° tan 47 tan 86°

$$\because$$ $$tan(90-\theta) = cot\theta$$

=> $$tan 4^{\circ} = tan(90^{\circ}-86^{\circ}) = cot 86^{\circ}$$

Similarly, $$tan 43^{\circ} = cot 47^{\circ}$$

=> $$(cot 86^{\circ} \times tan 86^{\circ}) * (tan 47^{\circ} \times cot 47^{\circ})$$

Using, $$tan\theta cot\theta$$ = 1

=> 1*1 = 1

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