\(sin\theta = {P\over H}\) || \(cos\theta = {B\over H}\) || \(tan\theta = {P\over B}\)
\(cosec\theta = {H\over P}\) || \(sec\theta = {H\over B}\) || \(cot\theta = {B\over P}\)
Trigonometric Ratio Relationships
\(sin\theta = {1\over cosec\theta}\) || \(cosec\theta= {1\over sin\theta}\)
\(cos\theta= {1\over sec\theta}\) || \(sec\theta= {1\over cos\theta}\)
\(tan\theta= {1\over cot \theta}\) || \(cot\theta= {1\over tan \theta}\)
\(tan\theta= {sin\theta\over cos \theta}\) || \(cot\theta= {cos\theta\over sin \theta}\)
\(sin^2\theta+cos^2\theta =1\)
\(sec^2\theta-tan^2\theta = 1\)
\(cosec^2\theta - cot^2\theta= 1\)
\(sin\theta=cos({\pi\over2}-\theta)\) || \(cos\theta=sin({\pi\over2}-\theta)\)
\(tan\theta=cot({\pi\over2}-\theta)\) || \(cot\theta=tan({\pi\over2}-\theta)\)
\(sec\theta=cosec({\pi\over2}-\theta)\) || \(cosec\theta=sec({\pi\over2}-\theta)\)
\(sin(-\theta)=-\space sin(\theta)\)
\(cos(-\theta)=cos(\theta)\)
\(tan(-\theta)=-\space tan(\theta)\)
\(cot(-\theta)=-\space cot(\theta)\)
\(sec(-\theta)= sec(\theta)\)
\(cosec(-\theta)= -\space cosec(\theta)\)
\(sinA+sinB=2\times sin({A\space+\space B\over2})\times cos({A\space-\space B\over2})\)
\(sinA-sinB=2\times sin({A\space-\space B\over2})\times cos({A\space+\space B\over2})\)
\(cosA+cosB=2\times cos({A\space+\space B\over2})\times cos({A\space-\space B\over2})\)
\(cosA-cosB=-2\times sin({A\space+\space B\over2})\times sin({A\space-\space B\over2})\)
\(sinA\times sinB={1\over2}[cos(A\space-\space B)-cos(A\space+\space B)]\)
\(cosA\times cosB={1\over2}[cos(A\space-\space B)+cos(A\space+\space B)]\)
\(sinA\times cosB={1\over2}[sin(A\space+\space B)+sin(A\space-\space B)]\)
\(cosA\times sinB={1\over2}[sin(A\space+\space B)-sin(A\space-\space B)]\)
\(sin\space (A+B)= sin A\space cos B \space +\space cosA\space sin B\)
\(sin\space (A-B)= sin A\space cos B \space -\space cosA\space sin B\)
\(cos\space (A+B)= cos A\space cos B \space -\space sinA\space sin B\)
\(cos\space (A-B)= cos A\space cos B \space +\space sinA\space sin B\)
\(tan\space (A+B)= {tan A\space +\space tan B\over 1\space -\space tanA\space tanB}\)
\(tan\space (A-B)= {tan A\space -\space tan B\over 1\space +\space tanA\space tanB}\)
\(sin\space 2\theta = 2\space sin\theta \space cos \theta\)
\(cos\space 2\theta = cos^2\theta-sin^2\theta\)
\(cos\space 2\theta = 1- 2sin^2\theta\)
\(cos\space 2\theta = 2\space cos^2\theta-1\)
\(tan\space 2\theta= {2\space tan\theta\over1-tan^2\theta}\)
\(sin\space 3\theta = 3\space sin\theta-4\space sin^3\theta\)
\(cos\space 3\theta = 4\space cos^3\theta-3\space cos\theta\)
\(tan\space 3\theta={3\space tan\theta-tan^3\theta\over 1- 3\space tan^2\theta}\)
\(sin\space {\theta\over2}=\pm\sqrt{1-cos\theta\over2}\)
\(cos\space {\theta\over2}=\pm\sqrt{1+cos\theta\over2}\)
\(tan\space {\theta\over2}=\pm\sqrt{1-cos\theta\over 1+ cos\theta}={1-cos\theta\over sin\theta} = {sin\theta\over 1+cos\theta}\)
\(sin^2\space \theta= {1-cos\space 2 \theta\over2}\)
\(cos^2\space \theta= {1+cos\space 2 \theta\over2}\)
\(tan^2\space \theta= {1\space -\space cos\space 2 \theta\over1\space + \space cos\space 2\theta}\)
\({a\over sin\space A}={b\over sin\space B}= {c\over sin\space C}\)
\(cosA= {{b^2+c^2- a^2}\over 2bc }\)
\(cosB= {{a^2+c^2- b^2}\over 2ac }\)
\(cosC= {{b^2+a^2- c^2}\over 2ab }\)
\({a\space -\space b\over a\space +\space b}={tan[{1\over2}(A\space-\space B)]\over tan [{1\over2}(A\space +\space B)]}\)
\(S=r\theta\)
♦ Value of equation of type:- \( cosθ.cos2θ.cos4θ.cos8θ ....cos2^{n-1}θ \) is \({sin2^{n}θ\over 2^n.Sinθ.}\) ; where n is the number of terms.
♦ Value of equation type is tanθ.tan(60° + θ).tan(60° - θ) = tan3θ
\(e^{i\theta}=cos\theta+i\space sin\theta\)
\((r(cos\theta+i\space sin\theta))^n=r^n(cos\space n\theta+i\space sin\space n\theta)\)
\({a\space+\space b\over c}={cos[{1\over2}(A\space-\space B)]\over sin({1\over2}C)}\)
\({a\space-\space b\over c}={sin[{1\over2}(A\space-\space B)]\over cos({1\over2}C)}\)