52nd Problem 2016

Geometry Level 2

cos ⁡ θ − csc ⁡ θ sin ⁡ θ − sec ⁡ θ = ? \large \dfrac { \cos { \theta -\csc { \theta } } }{ \sin { \theta } -\sec { \theta } } =?

Check out the set: 2016 Problems

tan ⁡ θ \tan\theta 2 tan ⁡ 2 θ 2\tan ^{ 2 }{ \theta } cot ⁡ 2 θ \cot^{ 2 }\theta cot ⁡ θ \cot\theta

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Marta Reece
Jul 19, 2017

cos ⁡ θ − csc ⁡ θ sin ⁡ θ − sec ⁡ θ = ( sin ⁡ θ cos ⁡ θ − 1 ) 1 sin ⁡ θ ( sin ⁡ θ cos ⁡ θ − 1 ) 1 cos ⁡ θ = cos ⁡ θ s i n θ = cot ⁡ θ \dfrac { \cos { \theta -\csc { \theta } } }{ \sin { \theta } -\sec { \theta } }=\dfrac{(\sin\theta\cos\theta-1)\frac1{\sin\theta}}{(\sin\theta\cos\theta-1)\frac1{\cos\theta}}=\dfrac{\cos\theta}{sin\theta}=\cot\theta

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