Question

cos theta. sin theta - (sin^2 theta.cos theta / cosec theta) - (cos^2 theta.sin theta / sec theta)​

Answer 1

Answer:

' 0 ' is answer

Step-by-step explanation:

$cos\theta. sin \theta - (sin^2 \theta.cos \theta / cosec \theta) - (cos^2 \theta.sin \theta / sec \theta\\\\=>sin\theta.cos\theta-(sin^3\theta.cos\theta)-(cos^3\theta.sin\theta)$

Since,

        $cosec\theta=\frac{1}{sin\theta}\\\\ sec\theta=\frac{1}{cos\theta}$

$=>sin\theta.cos\theta(1-sin^2\theta-cos^2\theta)\\\\=>sin\theta.cos\theta(1-(sin^2\theta+cos^2\theta))\\\\=>sin\theta.cos\theta(1-1)\\\\=>sin\theta.cos\theta(0)\\\\=>0$

Since we have Trigonometric identity , $sin^2\theta+cos^2\theta=1$

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