Question

if sin4theta - cos4theta =k4, then sin2theta - cos2theta​

Answer 1

ANSWER:

$\sin^{2}θ - \cos^{2}θ= {k}^{4}$

Answer 2

$(\sin^2\theta -\cos^2\theta )= k^4$

Step-by-step explanation:

given that

$\sin^4\theta -\cos ^4\theta = k^4$

using the identity

$a^2-b^2= (a+b) (a-b)$..(1)

therefore

$(\sin^2\theta)^2 -(\cos ^2\theta)^2 = k^4$

using 1

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

we know that

$(\sin^2\theta +\cos^2\theta ) =1$

therefore ,

$1 \times (\sin^2\theta -\cos^2\theta )= k^4$

$(\sin^2\theta -\cos^2\theta )= k^4$

hence , $(\sin^2\theta -\cos^2\theta )= k^4$

#Learn more:

Sin4theta + sin2theta cos4theta=sin2theta

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