trignonmetry

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6. Prove that tan λ cos^2 λ + sin^2λ/sin λ
= cos λ + sin λ

10. Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ

17.Prove that sin^2w-cos^2w/tan w sin w + cos w tan w = cos w-cot w cos w

23. Find a counterexample to shows that the equation sec a – cos a = sin a sec a is not an identity.

  • trignonmetry -

    PLEASE tell your classmates to use parentheses to clarify the problems!

    I think you mean
    (tan*cos^2 + sin^2)/sin
    = (sin*cos + sin^2)/sin
    = sin(cos+sin)/sin
    = cos+sin

    I think you mean
    (1+tan)/(1-tan)
    = (1+tan)^2/(1-tan^2)
    = (1+2tan+tan^2)/(1-tan^2)
    = (sec^2+2tan)/(1-tan^2)

    I think you mean
    (sin^2 - cos^2)/(tan*sin+cos*tan)
    = (sin-cos)(sin+cos)/(tan(sin+cos)
    = (sin-cos)/tan
    = sin*cot - cos*cot
    = cos-cos*cot

    always try simple values for counter-examples:
    a=0: 1-1 =? 0 -- yes
    a=pi: -1+1 =? 0 -- yes
    a=pi/4: √2 - 1/√2 =? 1/√2*√2 NO!

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