How do you simplify $f (θ) = 2 csc 2 θ - cos 2 θ + sec 2 θ$ $f(theta)=2csc2theta-cos2theta+sec2theta$ to trigonometric functions of a unit $θ$ $theta$ ?

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How do you simplify $f (θ) = 2 csc 2 θ - cos 2 θ + sec 2 θ$ $f(theta)=2csc2theta-cos2theta+sec2theta$ to trigonometric functions of a unit $θ$ $theta$ ?

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Answer 1 · 2016-07-18T05:05:16

f(t) = 2csc 2t - 2cos 2t + sec 2t
$A = \frac{2}{sin 2 t} = \frac{2}{2} sin t cos t = \frac{1}{sin t cos t}$ $A = 2/(sin 2t) = 2/2sin tcos t = 1/(sin tcos t)$
$B = - cos 2 t = - (1 - 2 {sin}^{2} t) = 1 - 2 {sin}^{2} t =$ $B = - cos 2t = -(1 - 2sin^2 t) = 1 - 2sin^2 t =$
$= (1 - \sqrt{2} sin t) (1 + \sqrt{2} sin t)$ $= (1 - sqrt2sint)(1 + sqrt2sin t)$
$C = \frac{1}{cos 2 t} = \frac{1}{1 - 2 {sin}^{2} t} = \frac{1}{(1 - \sqrt{2} sin t) (1 + \sqrt{2} sin t)}$ $C = 1/(cos 2t) = 1/(1 - 2sin^2 t) = 1/((1 - sqrt2sin t)(1 + sqrt2sin t))$
Finally,
f(t) = A + B + C
$f (t) = \frac{1}{sin t . cos t} + (1 - \sqrt{2} sin t) (1 + \sqrt{2} . sin t) + \frac{1}{(1 + \sqrt{2} sin t) (1 - \sqrt{2} sin t)}$ $f(t) = 1/(sin t.cos t) + (1 - sqrt2sint)(1 + sqrt2.sin t) + 1/((1 + sqrt2sint)(1 - sqrt2sin t))$

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How do you simplify $f (θ) = 2 csc 2 θ - cos 2 θ + sec 2 θ$ $f(theta)=2csc2theta-cos2theta+sec2theta$ to trigonometric functions of a unit $θ$ $theta$ ?

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How do you simplify f(θ)=2csc2θ−cos2θ+sec2θf(theta)=2csc2theta-cos2theta+sec2theta to trigonometric functions of a unit θtheta?

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How do you simplify $f (θ) = 2 csc 2 θ - cos 2 θ + sec 2 θ$ $f(theta)=2csc2theta-cos2theta+sec2theta$ to trigonometric functions of a unit $θ$ $theta$ ?