Question

If cosa + cos2a = 1 then, find the value of sin2a + sin4a ?

Answer 1

Step-by-step explanation:

CosA + cos^2A = 1

→cosA= 1-cos^2A

→cosA = sin^2A .

Now , sin^2A + sin^4A

= sin^2A + (cosA)^2 {cosA= sin^2A}

=sin^2 A + cos^2A

=1

Answer 2

Given = $\cos A + \cos^2A = 1$

To find : $sin^2A + \sin ^4 A$

Solution :

$\cos A + \cos^2A = 1\\\\\cos A = 1- \cos^2 A..(1)\\\\Cos A = \sin^2 A..(2)\\\\\therefore \\\\\sin^2A + \sin ^4 A \\\\\text{from 1 and 2 }\\\\\cos A + (cosA)^2\\\\\cos A + \cos^2A \\\\=1$

hence , the value is 1

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