Question

if costheta - sintheta = root 2sintheta then show that costheta + sintheta = root2 costheta​

Answer 1

Answer:

proved

Step-by-step explanation:

square on both sides first in first equation i.e  [cos Ф- sin Ф=√2sinФ]  then put the value of 2sinФcosФ in second equation after squaring 2 equation

MATHEMATICAL EQUATIONS

⇒COSФ - SINФ =√2SINФ

SQAUARING BOTH SIDES WE GET

⇒COS²Ф + SIN²Ф - 2SINФCOSФ=2SINФ  

NOW ,

⇒1 - 2SINФCOSФ = 2SINФ

WE GET,

⇒2SINФCOSФ= 1-2SINФ .........           (1)

NOW SQUARING IN 2 ND EQUATION

⇒COS²Ф+SIN²Ф+2SINФCOSФ

⇒1+2SINФCOSФ

NOW PUTTING THE VALUE OF 2SINФCOSФ WE GET

⇒1+1-2SINФ

⇒2-2SINФ

AFTERWARDS WE CAN CONVERT IT INT0 √2COSФ