If cosA + sinA=root of 2.cosA then prove that cosA-sinA=root of 2.sinA. Here root is only for 2 not for sin and cos
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Given, cos A + sin A = root 2. cos A
Squaring on both sides we get ...
(cos a + sin a)^2 = 2 cos^2 a
cos^2 a - sin^2 a = 2 sin a cos a
(cos a+sin a)(cos a-sin a) = 2 sin a cos a
replace cos a + sin a with root 2 cos a(given in question)
cos a - sin a = 2 sin a cos a/ root 2 cos a
= root 2 sin a
Squaring on both sides we get ...
(cos a + sin a)^2 = 2 cos^2 a
cos^2 a - sin^2 a = 2 sin a cos a
(cos a+sin a)(cos a-sin a) = 2 sin a cos a
replace cos a + sin a with root 2 cos a(given in question)
cos a - sin a = 2 sin a cos a/ root 2 cos a
= root 2 sin a
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