Question

sinA+cosA=1 to prove cosA-sinA= +-1​

Answer 1

Answer:

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Answer 2

Answer:

To prove-cosA-sinA= +-1

Step-by-step explanation:

We have:

(cos A – sin A)(cos A – sin A) = cos A cos A + sin A sin A – 2 cos A sin A

(cos A + sin A)(cos A + sin A) = cos A cos A + sin A sin A + 2 cos A sin A

Thus,

(cos A – sin A)(cos A – sin A) + (cos A + sin A)(cos A + sin A)

= 2 cos A cos A + 2 sin A sin A = 2

If cos A + sin A = 1, we obtain

(cos A – sin A)(cos A – sin A) + 1 = 2, or

(cos A – sin A)(cos A – sin A) = 1, whence

cos A – sin A = ± 1