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Quotient Trigonometric identitiesIn this section we will discuss the quotient trigonometric identities and their proofs.The quotient identities on trigonometry are as follows : 1) $tan \Theta = \frac{sin \Theta}{cos \Theta}$ 2) $cot \Theta = \frac{cos \Theta}{sin \Theta}$ Proof : Let a revolving ray start from OX and revolve into the position OP to trace out any angle $\Theta$ in any of the foru quadrants. From 'P' draw perpendicular to xaxis. 1) In the right angled triangle OMP, we have, $sin \Theta = \frac{PM}{OP}$ (i) $cos \Theta = \frac{OM}{OP}$ (ii) Now dividing equation (i) by (ii) $\frac{sin \Theta}{cos \Theta} = \frac{\left ( {\frac{PM}{OP}} \right )}{\left ({\frac{OM}{OP}} \right )}$ = ${\left ( {\frac{PM}{OP}} \right )}\times{\left ({\frac{OP}{OM}} \right )}$ = $\frac{PM}{OM}$ = $tan \Theta$ ∴ $\frac{sin \Theta}{cos \Theta} = tan \Theta$ 2) In the right angled triangle OMP, we have, $sin \Theta = \frac{PM}{OP}$ (i) $cos \Theta = \frac{OM}{OP}$ (ii) Now dividing equation (ii) by (i) $\frac{cos \Theta}{sin \Theta} = \frac{\left ( {\frac{OM}{OP}} \right )}{\left ({\frac{PM}{OP}} \right )}$ = ${\left ( {\frac{OM}{OP}} \right )}\times{\left ({\frac{OP}{PM}} \right )}$ = $\frac{OM}{PM}$ = $cot \Theta$ ∴ $\frac{cos \Theta}{sin \Theta} = cot \Theta$ Quotient trigonometric identities1) $tan \Theta \times cos \Theta = sin \Theta$2) $cot \Theta \times sin \Theta = cos \Theta$ From Quotient trigonometric identities to Home Covid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! Covid19 has affected physical interactions between people. Don't let it affect your learning.
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