Question

Simplify tan 75° + cot 75°

Answer 1

tan75° + cot75°

= sin75°/cos75° + cos75°/sin75°

= (sin75° . sin75° + cos75° . cos75°)/(cos75° . sin75°)

= (sin²75° + cos²75°)/(cos75° . sin75°)

we know, sin²x + cos²x = 1
so, sin²75° + cos²75° = 1

= 1/(cos75° . sin75°)

= 2/(2sin75°. cos75°)

we know, 2sinA.cosA = sin2A
so, 2sin75°. cos75° = sin2(75°) = sin150°

= 2/sin150°

= 2/sin(180° - 30°)

= 2/sin30°

= 2/(1/2)

= 4

hence, answer is 4

Answer 2

GIVEN:-

tan75° + cot75°

=> sin75°/cos75° + cos75°/sin75°

=> (sin75° . sin75° + cos75° . cos75°)/(cos75° . sin75°)

=> (sin²75° + cos²75°)/(cos75° . sin75°)

we know, sin²x + cos²x = 1
so, sin²75° + cos²75° = 1
2sinA.cosA = sin2A
so, 2sin75°. cos75° = sin2(75°) = sin150°

=> 1/(cos75° . sin75°)

=> 2/(2sin75°. cos75°)

=> 2/sin150°

=> 2/sin(180° - 30°)

=> 2/sin30°

=> 2/(1/2)

=> 4