Question

(1-Tan)^2+(1-Cot)^2=(Sec-Cosec)^2 Prove

Answer 1

Answer:

( 1 - Tan)² + (1 - Cot)² = (Sec - Cosec)²

Step-by-step explanation:

(1-Tan)^2+(1-Cot)^2=(Sec-Cosec)^2 Prove

LHS

= ( 1 - Tan)² + (1 - Cot)²

=  ( 1 - Sin/Cos)² + (1 - Cos/Sin)²

= (Cos - Sin)²/Cos²  + (Sin - Cos)²/Sin²

= (Cos - Sin)² ( 1/Cos² + 1/Sin²)

=  (Cos - Sin)² (Sin² + Cos²)/Cos²Sin²

= (Cos - Sin)² /Cos²Sin²

= ((Cos - Sin)/CosSin )²

= (Cos/CosSin - Sin/CosSin)²

= (1/Sin - 1/Cos)²

= (Cosec - Sec)²

= (Sec - Cosec)²

= RHS

QED

Proved

( 1 - Tan)² + (1 - Cot)² = (Sec - Cosec)²

Answer 2

Answer:

Step-by-step explanation:

LHS

= ( 1 - Tan)² + (1 - Cot)²

=  ( 1 - Sin/Cos)² + (1 - Cos/Sin)²

= (Cos - Sin)²/Cos²  + (Sin - Cos)²/Sin²

= (Cos - Sin)² ( 1/Cos² + 1/Sin²)

=  (Cos - Sin)² (Sin² + Cos²)/Cos²Sin²

= (Cos - Sin)² /Cos²Sin²

= ((Cos - Sin)/CosSin )²

= (Cos/CosSin - Sin/CosSin)²

= (1/Sin - 1/Cos)²

= (Cosec - Sec)²

= (Sec - Cosec)²

= RHS