Trigonometry Practice Test 2

© examsiri.com

Question : 5 of 22

Marks: +1, -0

If

\cosα+\sin α=√2\cos α

then what is the value of

\cosα-\sinα?

$√2 \cosα$
$√2 \sinα$
$√ 2$
1
None of these

Solution:

\cosα+\sin α=√2\cos α

On squaring both sides, we get:

\cos^2α+\sin^2 α+2\sin α\cosα= 2\cos^2 α

1+2\sin α\cosα= 2\cos^2 α

2\sin α\cosα= 2\cos^2 α-1

Now,

\cosα-\sinα

=√{\sin^2α+\cos^2α-2\sinα\cosα}

=√{1-2\cos^2α+1}=√2\sinα

© examsiri.com

Go to Question:

Prev Question

Next Question