Simplify and express as a constant or a single function of the given angle. Show all work (a) 1-sin^2 Pheta/ Cos^2 Pheta (b) Csc3PhetaTan3PhetaCos3Pheta

2 Answers

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

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(1) `(1-sin^2theta)/(cos^2 theta)`

From the Pythagorean identity `sin^2theta+cos^2theta=1` we get `cos^2theta=1-sin^2theta`

Then `(1-sin^2theta)/(cos^2theta)=(cos^2theta)/(cos^2theta)=1`

(2) `csc3thetatan3thetacos3theta`

We use the reciprocal identities: `cscx=1/(sinx),tanx=(sinx)/(cosx)` . Substituting we get:


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pramodpandey | College Teacher | (Level 3) Valedictorian

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A) we have given




=Cos(2p theta)sec^2(ptheta)

B). Cosec(3ptheta)tan(3ptheta)cos(3ptheta)