cos4θ – sin4θ =A) 1 – 2sin2θB) 2sin2θC) secθD) cosecθ

1.	cos4θ – sin4θ =A) 1 – 2sin2θB) 2sin2θC) secθD) cosecθ
Answer» Correct option is: A) \(1-2 \,sin^2\theta\) \(cos^4 \theta – sin^4 \theta =\) \((cos^2\theta)^2 - (sin^2\theta)^2\) = \((cos^2\theta - sin^2\theta) (cos^2\theta + sin^2\theta)\) (\(\because\) \(a^2-b^2 = (1-b) (a+b))\) = \(cos^2\theta - sin^2\theta \) (\(\because\) \(\cos^2\theta + sin^2\theta =1\)) = \((1-sin^2\theta) - sin^2\theta \) ( \(\because\) \(cos^2\theta = 1-sin^2\theta\) ) = \(1-2 \,sin^2\theta\) Correct option is: A) 1 – 2sin²θ

Answer»

Correct option is: A) \(1-2 \,sin^2\theta\)

\(cos^4 \theta – sin^4 \theta =\) \((cos^2\theta)^2 - (sin^2\theta)^2\)

= \((cos^2\theta - sin^2\theta) (cos^2\theta + sin^2\theta)\)

(\(\because\) \(a^2-b^2 = (1-b) (a+b))\)

= \(cos^2\theta - sin^2\theta \) (\(\because\) \(\cos^2\theta + sin^2\theta =1\))

= \((1-sin^2\theta) - sin^2\theta \) ( \(\because\) \(cos^2\theta = 1-sin^2\theta\) )

= \(1-2 \,sin^2\theta\)

Correct option is: A) 1 – 2sin²θ

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