Question

Can anyone please solve this?

Answer 1

Hope this answer may help you

Answer 2

cosA + sinA = 1 (equation 1)

Squaring both sides, we get,

(cosA + sinA)^2 = 1

cos^2 A + sin^2 A + 2 cosA sinA = 1

1 + 2 cosA sinA = 1 { since cos^2 A + sin^2 A = 1 (identity)}  

2 cosA sinA = 0

cosA sinA = 0

Now, either

cos A = 0

OR

sin A = 0

If sin A = 0 

then substituting the value of sin A = 0 in (equation 1),

cos A + 0 = 1

cos A = 1

If cos A = 0

then substituting the value of cos A = 0 in (equation 1),

0 + sin A = 1

sin A = 1

Now we have two situations,

1))) If sin A = 0, then cos A = 1

2))) If cos A = 0, then sin A = 1

Considering situation 1 and substituting the values in cos A – sin A

sin A = 0 and cos A = 1

Therefore, 

1 – 0 = 1

Situation 1 yields the answer as 1

Considering situation 2 and substituting the values in cos A – sin A

cos A = 0 and sin A = 1

Therefore, 

0 – 1 = -1

Situation 2 yields the answer as -1

 

Therefore we proved that if cosA+sinA = 1 then, cosA-sinA = 1 or -1.