Question

Prove that 2tan70 = tan80-tan10

Answer 1

Answer:

Step-by-step explanation:

Tan70=tan80-tan10/1+tan80tan10---(1)

As(tan(A-B)=tanA-tanB/1+tanAtanB)

Now

Tan80=cot(90-80)

Tan80=cot10. (Complementary angles)

Now in(1)

Tan70=tan80-tan10/1+cot10tan10

Tan70=tan80-tan10/1+1. (Cot×tan=1)

Tan70=tan80-tan10/2

2tan70=tan80-tan10. Hence proved

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Answer 2

Answer:

$tan80^{o} =2tan70^{o}+tan10^{o}$

Step-by-step explanation:

Given:

$tan80^{o} =2tan70^{o}+tan10^{o}$

To prove:

$tan80^{o} =2tan70^{o}+tan10^{o}$

Solution:

The trigonometric function is involved in the question. One of the trigonometric ratios is the tangent. In this case, we can obtain the necessary value of angle by taking the inverse tangent function on both sides of a given function, then utilising the stated angle of trigonometric ratios.

The trigonometric table's tan(A+B) formula will be utilised to make two factors, which when solved will give us the answer to the question. The following formula will then be used to answer the question.The ratio of a right-angled triangle's adjacent and opposite sides, often known as the tangent or tan, is one of the trigonometric functions.

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

From the question,

$tan80^{o} =tan(10+70)^{o} \\=\frac{tan(10+70)}{1-tan10tan70)} \\tan80-tan10tan70tan80=tan10+tan70\\tan80-tan70=tan10+tan70\\tan80=tan10+2tan70$

Hence proved

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