Question

If cos 0 + sin 0 = 1. prove that cos 0 - sin 0 = +1.​

Answer 1

Step-by-step explanation:

We have,

$\tt \: cos( \theta) + sin( \theta) = 1$

$\tt \implies \:( cos( \theta) + sin( \theta))^{2} = 1$

$\tt \implies \: cos^{2} ( \theta) + sin^{2} ( \theta) + 2 cos( \theta) sin( \theta) = 1$

$\tt \implies \:1 + 2 cos( \theta) sin( \theta) = 1$

$\tt \implies \:2 cos( \theta) sin( \theta) = 0$

$\tt \implies \: sin(2 \theta) = 0$

$\tt \implies \: \theta = 0$

Now,

$\tt \: cos (\theta) - sin( \theta) = cos (0^{ \degree} ) - sin( 0 ^{ \degree} )$

$\tt \: = 1 - 0 = 1$