Question

if tanq=2 then tan2q will be

Answer 1

Solution:

We know that,

$\tt \implies \tan(2x) = \dfrac{2 \tan(x) }{1 - { \tan}^{2}(x)}$

Here, it's given that,

$\tt \implies \tan(x) = 2$

Putting the value of tan(x) in the formula, we get,

$\tt \implies \tan(2x) = \dfrac{2 \times 2 }{1 - {2}^{2}}$

$\tt \implies \tan(2x) = \dfrac{4}{1 -4}$

$\tt \implies \tan(2x) = \dfrac{4}{ - 3}$

$\tt \implies \tan(2x) = - \dfrac{4}{3}$

Answer:

• tan(2x) = -4/3

Additional Information:

1. Relationship between sides.

• sin(x) = Height/Hypotenuse.
• cos(x) = Base/Hypotenuse.
• tan(x) = Height/Base.
• cot(x) = Base/Height.
• sec(x) = Hypotenuse/Base.
• cosec(x) = Hypotenuse/Height.

2. Square formulae.

• sin²x + cos²x = 1.
• cosec²x - cot²x = 1.
• sec²x - tan²x = 1

3. Reciprocal Relationship.

• sin(x) = 1/cosec(x).
• cos(x) = 1/sec(x).
• tan(x) = 1/cot(x).

4. Cofunction identities.

• sin(90° - x) = cos(x) and vice versa.
• cosec(90° - x) = sec(x) and vice versa.
• tan(90° - x) = cot(x) and vice versa.

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Answer 2

✰ Question Given :

• ➲ If tanq=2 then tan2q will be ?

✰ Required Solution :

✯ Formula used Here :

• ➲ tan2q = 2tanq / 1 - tan²q

✯ According to Question :

• ➥ Now , Doing Evaluation

• ➥ tan2q = 2tanq / 1 - tan²q

• ➥ 2 × 2 / 1 - (2)²

• ➥ 4 / 1 - 4

• ➥ 4 / - 3

✰ Therefore :

➢ tanq = 2 then tan2q will be 4 / - 3

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