Question

prove that)(sin A + cos economy A) power 2 +(cos A+sec A) power 2 =7tan2A+cot2A ((note 7tan2A means 7tanA to the power 2 and same meaning for cot2A))

Answer 1

hi!
there are a few mistakes in the question
it should be (sin A + cosecA A)²+(cos A+sec A) ²= 7+tan²A+cot²A

we have LHS = (sin A + cosecA A)²+(cosA+secA)²

=> sin²A+cosec²A+2sinAcosecA+cos²A+sec²A+2secAcosA

=> 1 +cosec²A+2+sec²A+2 [since sin²A+cos²A=1 and secA=1/cosA , cosecA=1/sinA]

=> 1+1+cot²A+2+1+tan²A+2 [since cosec²A=1+cot²A , sec²A=1+tan²A]

=> 7+tan²A+cot²A=RHS

Answer 2

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