Question

Tan 75° + cot 75
°ans fast





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Answer 1

Answer:

4

Explanation:

Answer: tan 75° + cot 75° = 4

Let's prove tan 75° + cot 75° = 4

Explanation:

We can make use of trigonometric table to calculate LHS.

tan 75° = tan (30° + 45°)

Using the formula, tan (A + B) = (tan A + tan B) / (1 - tan A tan B)

tan (30° + 45°) = (tan 30°+ tan 45°) / (1 - tan 30° tan 45°)

= {(1/√3) + 1} / {1- (1/√3)(1)}

= (√3 + 1) / (√3 - 1)

Since, tan θ = 1/cot θ, therefore, tan 75° = 1/cot 75°

cot 75° = (√3 - 1) / (√3 + 1) (Since, tan 75° = (√3 + 1) / (√3 - 1))

Now, tan 75° + cot 75° = (√3 + 1) / (√3 - 1) + (√3 - 1) / (√3 + 1)

= {(√3 + 1)2 + (√3 - 1)2} / {(√3)2 - (1)2} (Using the identity (a + b) (a - b) = a2 - b2 in the denominator)

= (3 + 1 + 2√3 + 3 + 1 - 2√3) / (3 - 1) (Using the identity (a - b)2 = a2 + 2ab + b2 and (a + b)2 = a2 - 2ab + b2 in the numerator)

= 4

= RHS

Hence, proved tan 75° + cot 75° = 4

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