Question

(1+tan) ^2+(1+cot)^2=(sec+cosec) ^2​

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