Question

tan(x-30°)=cot(x+30°) find the value of x​

Answer 1

Answer:

check this out from below

Step-by-step explanation:

Answer 2

Answer :

x = 45°

Note :

• sin∅ and cos∅ are complement of each other , thus sin(90° - ∅) = cos∅ and cos(90° - ∅) = sin∅ .
• sec∅ and cosec∅ are complement of each other , thus sec(90° - ∅) = cosec∅ and cosec(90° - ∅) = sec∅ .
• tan∅ and cot∅ are complement of each other , thus tan(90° - ∅) = cot∅ and cot(90° - ∅) = tan∅ .

Solution :

• Given : tan(x - 30°) = cot(x + 30°)
• To find : x = ?

We have ;

=> tan(x - 30°) = cot(x + 30°)

=> tan(x - 30°) = tan[90° - (x + 30°)]

=> x - 30° = 90° - (x + 30°)

=> x - 30° = 90° - x - 30°

=> x + x = 90° - 30° + 30°

=> 2x = 90°

=> x = 90°/2

=> x = 45°

Hence , x = 45°.