Question

tan theta + cot theta ka whole square minus tan theta minus cot theta ka whole square is equal to 4 . prove lhs _ rhs​

Answer 1

Answer:-

To prove:

(tan A + Cot A)² - (tan A - Cot A)² = 4

Using (a + b)² = a² + b² + 2ab and (a - b)² = a² + b² - 2ab in LHS we get,

→ tan² A + Cot² A + 2*tan A * Cot A - (tan² A + Cot² A - 2*tan A*Cot A) = 4

→ tan² A + Cot² A + 2*tan A*Cot A - tan² A - Cot² A + 2*tan A*Cot A = 4

Using Cot A = 1/tan A we get,

→ 2*tan A*1/tan A + 2*tan A*1/tan A = 4

→ 2(1) + 2(1) = 4

→ 4 = 4

→ LHS = RHS.

Hence, Proved.