Question

sin(A+45)+cos(A+45)=√2cosa
answer with step by step​

Answer 1

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Answer 2

LHS=Sin(A+45)+Cos(A+45)

Now,we know,

Sin(A+45)=SinACos45+CosASin45

And,

Cos(A+45)=CisACos45-SinASin45

Then,LHS=(SinACos45+CosASin45)+(CosACos45-SinASin45)

=SinA(1/√2)+CosA(1/√2)+CosA(1/√2)-SinA(1/√2)

=2CosA(1/√2)

=√2CosA. {Since 2=√2*√2}