Question

if cos theta+sin theta=√2 sin theta, find cos theta- sin theta.​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

Let theta = A

cos A + sin A = √2 sin A

cos A = sin A (√2-1)

tan A = √2+1 ---------(I)

cos A - sin A = sin A ( cot A -1)

= sin A (√2-1-1) = (√2-2) sin A. -------(2)

From (I)

sin A/cos A = √2+1

sin A/ √(1-sin²A) = √2+1

Whole squaring both sides ,

sin² A/1-sin²A = (√2+1)

sin²A = (1-sin²A)(√2+1)

sin²A = √2 +1 -√2sin²A - sin ² A

sin²A (2+√2) = (√2+1)

sin²A = √2+1/2+√2

sin A = √(√2+1)/(2+√2)

From (2),

cos A -sin A = (√2-2){√(√2+1)/(2+√2)} ----- ( Answer).