Question

(cos2 θ/ sin θ) – cosec θ + sin θ = 0

Plzzz solve this plzzzzzz ​

Answer 1

Step-by-step explanation:

• Taking LHS and using sin²θ + cos²θ = 1 , we have,

LHS

$\longrightarrow \sf \: \frac{cos {}^{2} \theta}{sin \theta} - cosec \theta \: + \: sin \theta$

$\longrightarrow \sf \: ( \frac{cos {}^{2} \theta }{sin \theta} - cosec \theta) + sin \theta$

$\longrightarrow \sf \: ( \frac{cos {}^{2} \theta}{sin \theta} - \frac{1}{sin \theta} ) + sin \theta$

$\longrightarrow \sf \: ( \frac{cos {}^{2} \theta - 1}{sin \theta} ) + sin \theta$

$\longrightarrow \sf \: ( \frac{ - sin {}^{2} \theta }{sin \theta} ) + sin \theta$

$\longrightarrow \sf \: - sin \theta + sin \theta$

$\longrightarrow \sf 0 \: \: \green \bigstar$

RHS

• Hence Proved!!