Question

If coso +sino =root2coso, prove coso-sino= root2sino​

Answer 1

Step-by-step explanation:

cos theta+sin theta=√2cos theta then

cos theta-sin theta=√2sin theta

GIVEN,

cos theta+sin theta=√2cos theta

WE KNOW THAT,

cos^2 theta+sin^2 theta=1. : IDENTITY

THEN,

(cos theta+sin theta)(cos theta-sin theta)=2

(√2cos theta)(cos theta-sin theta)=1

(cos theta-sin theta)=1/√2cos theta

cos theta-sin theta=√2sin theta

HENCE,PROVED

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