Question

Prove that 1 + sin 2A + COS 2A÷1+sin2A-cos2A=tan(90-A)​

Answer 1

Answer:

) (1 + SIN2A - COS2A)/(1+SIN2A + COS2A) = TANA

 

SIN2A =2TANA/1+TAN2A      &  COS2A =1-TAN2A/1+TAN2A

PUTTING THESE

 LHS =(2TAN2A + 2TANA)/2TANA+2

       =TANA = RHS

2)   (SINA + SIN2A)/(1+COSA+COS2A)    =   TANA

 COS2A = 2COS2A - 1       &   SIN2A =2SINACOSA

AFTER PUTTING THESE

 

LHS = (SINA+2SINACOSA)/COSA+2COS2A

      =SINA(1+2COSA) / COSA(1+2COSA)

      =SINA/COSA=TANA =RHS

HENCE PROVED