Question

Prove: (sin A+ cosec A)2+(cos A + sec A) 2= 7+tan 2A+ cot2A​

Answer 1

Answer:

hii buddy ,

=> (sin A + cosec A)² + ( cos A + sec A)²

=> (sin A + 1/sin A)² + ( cos A + 1/cos A)²

=> sin² A + 1/sin² A + 2 + cos ² A + 1/ cos ² A + 2

=> sin ² A + cos ² A + 1 / sin ² A + 1/ cos ² A + 2 + 2

=> 1 +4 + cosec ² A + sec ² A

since , cosec ² A = 1+ tan ² A

& sec ² A = 1 + cot ² A

=> 1 + 4 + 1 + tan ² A + 1 + cot ² A

=> 7 + tan ² A + cot ² A

RHS = 7 + tan ² A + cot ² A

since , LHS= RHS

hence ,

proved

hope this helps