How do you prove tan(90°+a)=-cot(a)? Trigonometry Trigonometric Identities and Equations Fundamental Identities 1 Answer Konstantinos Michailidis Jul 17, 2016 We know that tan(90+a)=sin(90+a)/(cos(90+a))=[sin90*cosa+cos90*sina]/[cos90*cosa-sin90*sina]= [cosa]/[-sina]=-cotatan(90+a)=sin(90+a)cos(90+a)=sin90⋅cosa+cos90⋅sinacos90⋅cosa−sin90⋅sina=cosa−sina=−cota Note sin90=1 , cos90=0sin90=1,cos90=0 Answer link Related questions How do you use the fundamental trigonometric identities to determine the simplified form of the... How do you apply the fundamental identities to values of thetaθ and show that they are true? How do you use the fundamental identities to prove other identities? What are even and odd functions? Is sine, cosine, tangent functions odd or even? How do you simplify sec xcos (frac{\pi}{2} - x )secxcos(π2−x)? If csc z = \frac{17}{8}cscz=178 and cos z= - \frac{15}{17}cosz=−1517, then how do you find cot zcotz? How do you simplify \frac{\sin^4 \theta - \cos^4 \theta}{\sin^2 \theta - \cos^2 \theta} sin4θ−cos4θsin2θ−cos2θ using... How do you prove that tangent is an odd function? How do you prove that sec(pi/3)tan(pi/3)=2sqrt(3)sec(π3)tan(π3)=2√3? See all questions in Fundamental Identities Impact of this question 30970 views around the world You can reuse this answer Creative Commons License