Question

cos^2 theta / sin theta - cosec + sin theta=0​

Answer 1

S O L U T I O N :

$\underline{\bf{Given\::}}$

cos²Ф / sinФ - cosecФ + sinФ = 0

$\underline{\bf{Explanation\::}}$

Taking L.H.S .

$\mapsto\tt{\dfrac{cos^{2} \theta }{sin \theta } -cosec \theta + sin\theta }$

$\mapsto\tt{\dfrac{1-sin^{2} \theta }{sin \theta } -cosec \theta + sin\theta \:\:\:\underbrace{\therefore{\sf{ cos^{2} \theta = 1-sin^{2} \theta }}}}$

$\mapsto\tt{\dfrac{1}{sin \theta } - \dfrac{sin^2\theta}{sin\theta } - cosec \theta + sin\theta }$

$\mapsto\tt{\dfrac{1}{sin \theta } - \dfrac{\cancel{sin\theta} \times sin \theta }{\cancel{sin\theta }} - cosec \theta + sin\theta }$

$\mapsto\tt{cosec \theta - sin\theta - cosec \theta + sin \theta \:\: \: \underbrace{\sf{\therefore 1/sin \theta = cosec\theta }}}$

$\mapsto\tt{\cancel{cosec \theta -cosec \theta } \cancel{- sin \theta + sin \theta} }$

$\mapsto\tt{0 + 0}$

$\mapsto\bf{0 }$

Thus,

L.H.S = R.H.S  .