Question

Q.8. sin 0 (cosec 0 - sin0)
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Answer 1

= sin 0 cosec 0 - sin^2 0

= sin 0 * 1/ sin 0 - sin ^ 2 0 ( cosec 0 = 1/sin o)

= 1- sin^2 0

= cos ^ 2 0 is your answer...

Answer 2

$\sin\theta( \cosec\theta - \sin\theta) \\ \\ = \sin\theta( \frac{1}{ \sin\theta} - \sin\theta) \\ \\ = \sin\theta \times \frac{1}{ \sin\theta} - \sin\theta \times \sin\theta \\ \\ = 1 - { \sin\theta }^{2} \\ \\ = {\cos\theta}^{2}$

SOME IMPORTANT TRIGONOMETRY IDENTITIES :-

$1. {\sin\theta}^{2} + {\cos\theta}^{2} = 1 \\ \\ 2.{ \sec\theta}^{2} = 1 + { \tan\theta}^{2} \\ \\ 3. {\csc\theta }^{2} = 1 + {\sec\theta}^{2} \\ \\ 4. \sin\theta = \frac{1}{ \csc\theta } \\ \\ 5. \cos\theta = \frac{1}{ \sec\theta } \\ \\ 6. \tan\theta = \frac{1}{ \cot\theta}$