Question

If sinθ - cosθ =½
then, find the value of sinθ + cos θ​

Answer 1

Answer:

sin(x)-cos(x)=1/2 (*)

1/(sin(x)+cos(x))=?

1/(sin(x)+cos(x))=(sin(x)-cos(x))/(sin2(x)-cos2(x))=(1/2)/(-cos(2x))

From (*) it follows that 1-sin2(x)=1/4 (by taking square from sides)

sin(2x)=1-1/4=3/4

cos(2x)=√(1-9/16)=√7/4.

Therefore

1/(sin(x)+cos(x))=(1/2)/(-√7/4)=-2/√7.

Answer 2

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