Question

Given that sin θ =



then tan θ =………​

Answer 1

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★ Correct question :-

If sinθ = a/b , then find tanθ

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★ Solution :-

Given ,

• sinθ = a/b

We need to find ,

• tanθ = ?

Methods of finding tanθ

• Method 1 :- By finding the other side of triangle and finding.
• Method 2 :- By finding cosθ and using tanθ = sinθ/cosθ

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• Method 1 :-

sinθ = a/b

If sinθ = a/b , opposite side of θ = a & Hypotenuse of ∆ = b

Using Pythagoras theorem,

Hypotenuse² = Base² + Height²

→ b² = Base² + a²

→ b² - a² = Base²

→ Base² = √b² - a² = adjacent side

Now , finding tanθ

tanθ = Opposite/Adjacent

Where,

• Opposite = a
• Adjacent = √b² - a²

→ tanθ = a/√b² - a²

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• Method 2 :-

sinθ = a/b

As we know that

cosθ = ±√1 - sin²θ

Substituting we have ,

→ cosθ = √1 - (a/b)²

→ cosθ = √1 - a²/b²

→ cosθ = √b² - a²/b²

Using laws of exponents

• √(a/b) = √a/√b

Similarly

→ cosθ = √b² - a²/√b²

→ cosθ = √( b² - a² )/b

Now , substituting in tanθ = sinθ/cosθ

→ tanθ = { [ a/b ]/[ ( √b² - a² )/b ] }

→ tanθ = a/√b² - a²

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Hence , tanθ = a/√b² - a²

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