Question

if cosA-sinA=√2 sinA
then proove that cosA+sinA=√2cosA​

Answer 1

Answer:

Step-by-step explanation:

(cosA-sinA)=√2 sinA      

(cosA- sinA)/sinA = √2

cotA - 1 = √2

cotA = (√2 +1)  ........(i)

cosA+sinA=√2cosA​

(cosA+sinA)/cosA = √2

1 + tanA = √2

tanA = √2 - 1

1/cotA = √2 - 1

1/(√2 +1)  = (√2 - 1)

1 = (√2 - 1)(√2 +1)

1=1

hence proved LHS = RHS