Question

Find the value of cot75°​

Answer 1

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tan 75° = tan (45° + 30°)

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

= (1 + (1/√3)) /(1 - 1(1/√3))

= [(√3 + 1)/√3] / [(√3 - 1)/√3]

= (√3 + 1)/(√3 - 1)

Multiply by (√3 + 1) on both numerator and denominator.

= (√3 + 1)2/(√32 - 12)

= (3 + 1 + 2√3) / (3 - 1)

= (4 + 2√3) / 2

= 2 + √3

tan 15° = cot (90° - 15°)

tan 15° = cot 75°

Instead of finding the value of cot 75, let us find the value of tan 15.

tan 15° = tan (45° - 30°)

Using compound angle formula, we get

= (√3 - 1)/(√3 + 1)

Multiply by (√3 - 1) on both numerator and denominator.

= (√3 - 1)2/(√32 - 12)

= (3 + 1 - 2√3) / (3 - 1)

= (4 - 2√3) / 2

= 2 - √3

Cot 75°=2-√3

Answer 2

Step-by-step explanation:

Show that tan 75° + cot 75° = 4. Multiply by (√3 + 1) on both numerator and denominator. Instead of finding the value of cot 75, let us find the value of tan 15.