Question

write the table for trignometric identities

Answer 1

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$\mathfrak{question-}$$\textbf{write the table for trignometric identities}$

$\mathfrak{here \:is\:the\:solution\:for\:the \:question}$

$\mathbb {ANSWER}$

$\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$

$\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ \: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1 \end{minipage}}$

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Answer 2

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Reciprocal Identities

Sin θ = 1/Csc θ or Csc θ = 1/Sin θ

Cos θ = 1/Sec θ or Sec θ = 1/Cos θ

Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

Pythagorean Identities

sin2 a + cos2 a = 1

1+tan2 a = sec2 a

cosec2 a = 1 + cot2 a

Ratio Identities

Tan θ = Sin θ/Cos θ

Cot θ = Cos θ/Sin θ

Opposite Angle Identities

Sin (-θ) = – Sin θ

Cos (-θ) = Cos θ

Tan (-θ) = – Tan θ

Cot (-θ) = – Cot θ

Sec (-θ) = Sec θ

Csc (-θ) = -Csc θ

Complementary Angles Identities

Sin (90 – θ) = Cos θ

Cos (90 – θ) = Sin θ

Tan (90 – θ) = Cot θ

Cot ( 90 – θ) = Tan θ

Sec (90 – θ) = Csc θ

Csc (90 – θ) = Sec θ

Angle Sum and Difference Identities

Consider two angles , α and β, the trigonometric sum and difference identities are as follows:

sin(α+β)=sin(α).cos(β)+cos(α).sin(β)

sin(α–β)=sinα.cosβ–cosα.sinβ

cos(α+β)=cosα.cosβ–sinα.sinβ

cos(α–β)=cosα.cosβ+sinα.sinβ

tan(α+β)=tanα+tanβ1–tanα.tanβ

tan(α–β)=tanα–tanβ1+tanα.tanβ