The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions. The remaining trigonometric functions secant (sec), cosecant (csc), and cotangent (cot) are defined as the reciprocal functions of cosine, sine, and tangent, respectively. Trigonometric identities are equations involving the …

Here are a few examples I have prepared: a) Simplify: tanx cscx ×secx Apply the quotient identity tanθ = sinθ cosθ and the reciprocal identities cscθ = 1 sinθ and secθ = 1 cosθ. = sinx cosx 1 sinx × 1 cosx = sinx cosx × sinx 1 × 1 cosx = sin2x cos2x Reapplying the quotient identity, in reverse form: = tan2x b) Simplify: cscβ − ...

2015年9月22日 · Use the fact that tan (x) = sin (x)/cos (x) tanxcons = sinx/cosx *cosx/1 = sinx

2018年4月8日 · 1.) tan x = (sinx cos x) 2.) plug it in: (sinx cos x) + cosx 1 +sinx 3.) both sides must have a common denominator so: (sinx)(1 + sinx) (cosx)(1 +sinx) + (cosx)(cosx) (cosx)(1 +sinx) 4.) foil the equation (distribute): sinx + sin2x cosx + cosxsinx + cos2x cosx +cosxsinx 5.) add numerators: sinx + sin2x +cos2x cosx + cosxsinx 6.) then: cos2x + sin2x = 1 1 + sinx cosx(1 + sinx) 7.) cancel out 1 ...

2018年3月28日 · To prove the identity, you'll need these four, more basic identities: cscx=1/sinx cotx=cosx/sinx tanx=sinx/cosx sin^2x+cos^2x=1 To start the proof, use these identities to write everything in terms of sine and cosine.

2018年3月4日 · We have: LH S = cosx + sinxtanx and RH S = secx We change the LH S: cosx + sinx ⋅ sinx cosx = cosx + sin2x cosx = sin2x +cos2x cosx = 1 cosx = secx So LH S = RH S Hence, proved.

2018年6月2日 · tanx secx −cosx =? tanx = sinx cosx; secx = 1 cosx tanx secx −cosx = sinx cosx 1 cosx −cosx Multiplying numerator and denominator by cosx = sinx 1 − cos2x 1 ...

2016年3月26日 · sin (x)tan (x)+cos (x)=sec (x) sin (x)tan (x)+cos (x) = sin (x)sin (x)/cos (x)+cos (x) =sin^2 (x)/cos (x)+cos (x) =sin^2 (x)/cos (x)+cos^2 (x)/cos (x) = (sin^2 (x ...

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2018年4月10日 · I'm assuming you want us to prove that 1 tanx +tanx = 1 sinxcosx. 1 sinx cosx + sinx cosx = 1 sinxcosx cosx sinx + sinx cosx = 1 sinxcosx sin2x +cos2x sinxcosx = 1 sinxcosx 1 cosxsinx = 1 sinxcosx LH S = RH S As required. Hopefully this helps!