Question

please solve this question . Evalute it

Answer 1

$Given : sin \alpha * cos \alpha - \frac{sin\alpha cos(90 - \alpha) cos\alpha}{sec(90 - \alpha)} - \frac{cos\alpha sin(90 - \alpha)sin\alpha}{cosec(90 - \alpha)}$

$= > sin\alpha * cos\alpha - \frac{sin\alpha * cos\alpha * cos\alpha}{cosec\alpha} - \frac{cos\alpha * cos\alpha * sin\alpha}{sec\alpha }$

$= > sin\alpha * cos \alpha - \frac{sin \alpha * cos \alpha * cos\alpha}{\frac{1}{sin\alpha}} - \frac{cos\alpha * cos\alpha * sin\alpha}{\frac{1}{cos\alpha}}$

$= > sin\alpha * cos\alpha - sin\alpha * cos\alpha * sin^2\alpha - cos\alpha * sin\alpha * cos^2\alpha$

$= > sin\alpha * cos\alpha - cos\alpha * sin^3\alpha - cos^3\alpha * sin\alpha$

$= > sin\alpha * cos\alpha - sin\alpha cos\alpha (sin^2\alpha + cos^2\alpha)$

$= > sin\alpha * cos \alpha - sin\alpha * cos\alpha$

⇒ 0.

Hope it helps!