Question

tan²theate +cot²theate​

Answer 1

tan²Ө + cot²Ө = sin²Ө/cos²Ө + cos²Ө/sin²Ө

→ (sin⁴Ө + cos⁴Ө)/sin²Ө cos²Ө

→ (1 - 2sin²Ө cos²Ө)/sin²Ө cos²Ө {sin⁴x + cos⁴x = 1 - 2sinx cosx}

→ 4(1 - sin²2x)/sin²2x {sinx cosx = (sin 2x)/2 , 2sinx cosx = sin 2x}

→ 4(cos²2x)/sin²2x {1 - sin²x = cos²x}

→ 4 cot²2x