SSC CHSL Model Paper 18

Question : 66 of 100

Marks: +1, -0

For all real A, the simplified value of theexpression

\sin^6A + \cos^6A + 3\sin^2A \cos^2A

Solution:

Consider

\sin6^A + \cos^6A

(\sin^2A)^3 + (\cos^2A)^3

(\sin^2A + \cos^2A)(\sin^4A + \cos^4A

- \cos^2A \sin^2A)

1 ((\sin^2A)^2 + (\cos^2A)^2 -\cos^ 2A \sin^2A )

(\sin^2A + \cos^2A)^2 -2 \cos ^2A \sin^2A

- \cos^2A\sin^2A

\sin^6A + \cos^6A = 1- 3 \sin ^2A \cos^2A

⇒

\sin^6A + \cos^6A + 3\sin ^2A\cos^2A = 1

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