Question

tan80-tan10/tan70=how much

Answer 1

we know that ,
80 - 10 = 70
tan on both sides , we get ,
tan 80 - tan 10/1 + tan80*tan 10 = tan 70 ( tan ( A-B) = tan A - tanB /1 + tanA*tanB)
tan80 - tan 10 /tan 70 = 1+1 =2 ( since if A +B = 90 then tanA*tanB =1)
so the answer is 2.

Answer 2

Answer:

The value of $\frac{tan80 - tan10}{tan 70}$ = 2

Step-by-step explanation:

To find,

$\frac{tan80 - tan10}{tan 70}$

Recall the formula

tan(A-B)  = $\frac{tanA - tanB}{1+tanAtanB}$

tan(90 -A) = cot A

tan A = $\frac{1}{cotA}$

Solution

tan 70 = tan (80-10)

= $\frac{tan80 - tan10}{1+tan80tan10}$ (∵ tan(A-B)  = $\frac{tanA - tanB}{1+tanAtanB}$)

tan 70 = $\frac{tan80 - tan10}{1+tan80tan10}$

$\frac{tan80 - tan10}{tan 70}$ = 1+tan80tan10

= 1 + tan80tan(90-80)

= 1 +tan 80 cot 80 (∵ tan(90 -A) = cot A)

= 1 +1 (∵ tan A = $\frac{1}{cotA}$)

= 2

∴ $\frac{tan80 - tan10}{tan 70}$ = 2

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