Derivative Trig Functions

How do you prove #(1-\cos^2 x)(1+\cot^2 x) = 1#? How do you show that #2 \sin x \cos x = \sin 2x#? is true for #(5pi)/6#? How do you prove that #sec xcot x = csc x#? Desmos Classroom Activities Loading... The best answer to this question depends on the definitions you're using for the trigonometric functions: Unit circle: t correspond to point (x,y) on the circle x^2+y^2 =1 Define: sint = y, , cos t = x, , tant = y/x The result is immediate. Point (x,y) on the terminal side of t and r=sqrt(x^2+y^2) sint = y/r, , cos t = x/r, , tant = y/x sint/cost = (y/r)/(x/r)= (y/r)*(r/x) = y/x = tan t Right Transcript. Ex 2.2, 8 Write the function in the simplest form: tan−1 (cos⁡〖x − sin⁡x 〗/cos⁡〖x + sin⁡x 〗 ), 0 < x < π tan−1 (cos⁡〖x − sin Transcript. Ex 2.1, 12 Find the value of cos−1 (1/2) + 2 sin−1 (1/2) Solving cos−1 (𝟏/𝟐) Let y = cos−1 (1/2) cos y = (1/2) cos y = cos (𝝅/𝟑) ∴ y = 𝝅/𝟑 Since Range of cos−1 is [0 , 𝜋] Hence, the principal value is 𝝅/𝟑 (Since cos 𝜋/3 = 1/2) Solving sin−1 (𝟏/𝟐) Let y = sin−1 (1/2) sin y = 1/2 sin y = sin (𝝅/𝟔) ∴ y = 𝝅/𝟔 Since Range

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